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VOLUME XIV No. 1 


BULLETIN 
of the 
Buffalo Society of Natural 
Sciences 


~MAYA INSCRIPTIONS DEALING WITH 
VENUS AND THE MOON 
BY 


HERBERT J. SPINDEN 


Curator of Mexican Archaeology and Ethnology, Peabody Museum of Harvard 
University; Curator of Anthropology, Buffalo Museum of Science 


BUFFALO, NEW YORK 
1928 


Foreword 


The astronomical science of the Maya Indians of Yuca- 
tan and adjacent parts of Mexico and Central America 
must be recovered from inscriptions of the first centuries 
of the Christian era and from one native book that luckily 
survived the Spanish conquest. The present paper is an 
attempt to demonstrate the significance of many dates and 
calculations by sufficiency of coincidence after transcription 
into terms of European chronology. I have explained the 
correlation of the Maya and Gregorian calendars at length 
in other papers and have already shown numerous coin- 
cidences of an astronomical observatory at Copan con- 
structed to give certain sunset readings. 


The present paper is worked up from material brought 
together for a conference held under the auspices of the 
Carnegie Institution of Washington in December, 1927. 
This material includes a revised list of all known Maya 
dates—which I hope to bring to press in the near future 
since it corrects many previous errors. Although most of 
the research was done at the Peabody Museum of Harvard 
University, I embrace the opportunity to publish the results 
in the Bulletin of the Buffalo Society of Natural Sciences. 
This seems especially fitting since by a cooperative arrange- 
ment I am now on the scientific staff of both institutions. 
The XXIII Session of the International Congress of Ameri- 
canists at New York City, September 17-22, 1928, is a 
notable occasion for the presentation of this paper. 


HERBERT J. SPINDEN, 
Buffalo, August 30, 1928. 


Addendum 
(September 10, 1928) 


The days of the Lunar table of the Dresden Codex be- 
gin to coincide with solar eclipses about the middle of the 
Ninth century and continue for several centuries to state 
not only the eclipse visible in Yucatan and Central America 
but practically the entire series visible from any part of 
the Earth. During the First Empire the table, as it stands, — 
is displaced one lunation from actual eclipses. But during 
the Twelfth and Thirteenth centuries it functions prope es 
and with a usable record of past performances. rt 


Assuming that the table ends, and therefore bagines ; 
with 10 Cimi, there are two eclipses which may have served 
as the inauguration since they take place on such a day and ~ 
are separated from each other by a multiple of 11,960 days. — 
The first of these is a total eclipse with a line of centrality _ 
passing through Peru and northern Brazil and possibly — 
visible in Central America in a partial phase. The second 
is a total eclipse with a line of centrality passing through © 
Cuba and therefore visible in Yucatan in almost total phase. 
The first date is 11-1-15-3-6, 10 Cimi 19 Yaxkin, April 23, 
999 A. D., equivalent to Julian Day 2,086,050, and the ~ 
second and perhaps more likely one is 11-6-14-15-6, 10 Cimi — 
9 Mac, July 18, 1097 A. D., which is equivalent to Julian — 
Day 2,121,930. The first eclipse i is the 5239th in Oppolzer’s. 
Canon falling on Julian Day 2,086,050, at 17 h. 3.8 m., — 
world time. The second is described as having taken place | 
on Julian Day 2,121,929 at 20 h. 47.5 m., world time. iss 


Many other eclipses visible in Maya territory are 
properly placed for the named days of the table. a 


BOLLE EIN 


of the 


Buffalo Society of Natural Sciences 


VOLUME XIV No. 1 


Maya Inscriptions Dealing With Venus 
amd the Moon 


By H. J. SPINDEN 


INTRODUCTION 


This paper deals with inscriptions on ancient Maya monuments 
and with passages in the Maya book called the Dresden Codex which 
relate to Venus and the Moon. The transcription of dates is in 
accordance with the day-for-day correlation of Maya and European 
calendars fully explained in my Reduction of Mayan Dates. While 
this correlation has been accepted by several leading Maya scholars 
on the proofs already presented, others have hesitated principally 
because the dates given in the Dresden Codex in connection with the 
Venus calendar do not fall into obvious agreement with significant 
appearances of this planet and because the statements in the Supple- 
mentary Series of glyphs, which follow the Initial Series dates on 
monuments of the First Empire do not agree superficially with true 
positions of the Moon at the stated times.” 


ey *Papers of the Peabody Museum of American Archaeology and Ethnology, Harvard 
University, Vol. VI, No. 4, Cambridge, 1924. The original announcement of the 
correlation was made in 1919. 


“At a conference held by the Carnegie Institution of Washington in December, 
1927, the opposition of John E. Teeple was based on the matter of Venus and the 
Moon while Eric Thompson withdrew his rival correlation in view of the new 
evidence presented. Morley’s transcription of dates, while not of the day-for-day type 
necessary for astronomical uses, generally results in the same Christian year as the 
one under discussion. Tozzer and Blom have used the day-for-day adjustment but 
without much critical comment, and foreign students have mostly been non-commital. 
Juan Martinez y Hernandez of Yucatan has argued a rival correlation resting on a 
re-consideration of double datings and other historical evidence of the Sixteenth 
century. 

John E. Teeple has written the following articles in the American Anthropologist, 
1925-27. Maya Inscriptions: Glyphs C, D and E of the Supplementary Series (N. S. 
xxvii, pp. 105-115). Maya Inscriptions: Further Notes on the Supplementary Series 
(N. S. xxvii, pp. 544-549). Maya Inscriptions: The Venus Calendar and another 
Correlation (N. S. xxix, pp. 278*-282*) and Maya Inscriptions IV (idem, pp. 
283*-291*). 

Other recent correlations are by: 

Juan Martinez Hernandez, Paralelismo entre los calendarios Maya y Azteca, 
Diario de Yucatan, Feb. 7, 1926. 

J. Eric Thompson: A Correlation of the Mayan and European Calendars. 
Pub. ie Field Museum of Natural History, 1927. (Anthropological Series Vol. xvii, 
No. 1. 

These are based on a structural possibility fully discussed by Morley and myself, 
namely the identification of Katun 13 Ahau of the Sixteenth century with the . 
position 11-16- 0- 0- 0, 13 Ahau 8 Xul instead of with the position 12- 9- 0- 0- 0, 
13 Ahau 8 Kankin. The only authority for this arrangement is page 66 of the 
Chronicle of Oxkutzcab, which is contradictory of much important evidence. Martinez 


(Continued on bottom of page 6) 


Eu VENUS AND THE MOON 


The true basis of Maya chronology is not one of the severe 
calendars—whethéftof the civil year, the Moon, Venus, Mars, or pee 
some other planet—but it is the continuous and inviolate count OF os 
days which finds its nearest European counterpart in the Julian Day © 
system of astronomers. In this day count the Mayas seem to have ~ 
kept an ephemeris or journal of mundane and celestial events. Inter- 
vals between recurring phenomena, such as new moons, or solstices, 
or heliacal risings of planets, were obtainable from this day count by” 
simple averages. Indeed astronomers during the early centuries of 
the Maya civilization seem to have had sufficient data for compiling — 
various kinds of order in error among the planetary movements and 
may well have reached most interesting conclusions on the nature of 
the universe. 


Maya CALENDARS WITHOUT INTERCALATION — 


We have evidence that the early Mayas formulated a series of 
calendars for civil and religious use, basing them on the mean times. 
of apparent or synodic revolutions of the Earth around the Sun, of 
the Moon around the Earth and of several planets, including Venus, 
around the Sun. About the only evidence, so far deduced, that the 


1The Maya Long Count is first of all merely the succession of index ieee ; 
following from a formal zero day in much the same fashion that the year count of the 
Christian Era is a succession of index numbers following from a formal zero year, 
namely the one in which Christ was supposed to have been born. Days in these 
Christian years are designated by the short cycle of the week and by positions in the 
several months. Similarly in the Maya system days are differentiated by a_ cycle 
which is, however, much longer than our week, since it consists of a permutation of Ve 
13 numbers and 20 day names, making 260 changes. The Maya day designated by — 
one of the 13 numbers combined with one of the 20 names—1 Imix, 4 Ahau, 13 Akbal, 
etc.—is stated to eereey a definite position in a civil year which consists of 18 see: — 
of 20 days each plus five complementary days, making 365 days in all. ; 


A complete Maya date can be written thus: 
1,253,912, 10 Eb 0 Yaxkine 


It might be read “A day called Eb associated with the number 1, which is. one iat 
260 ways in which a day can be named, occupies the zero position in a month c fan 
Yaxkin, which is one of 365 positions in the civil year, and it is exactly 1,253, 912 *t 
days distant from the zero day of the Mundane era which is 4 Ahau 8 Cumhu.” 

The number alone counted forward from the Mundane era will recover ‘ie / and 
month position. Without the number the ‘calendar round” statement 1 Eb 0 aus 
recurs at intervals of 18,980 days (52 X 365 days). 


As a rule we do not write the number according to the Arabic system but in 
system which preserves the Maya notational units. Thus the above date is generally 
written 8-14- 3- 1-12, 1 Eb 0 Yaxkin. Here the highest place values are at the 
left and we have 8 X 144,000; 14 X 7,200; 3 X 360; 1X 20 and 12 x 1, which 
reduce to 1,253,912. Also ‘the numbers are generally read with Maya designatio 
for the place values, namely 8 baktuns, 14 katuns, 3 tuns, 1 uinal and 12 kins for) he 
example before us. ; >. 


(Continued from bottom of page 5) 
also makes use of a double date in which he makes two emendations, one of: never, 
_days and the other of several years in the Julian equivalent to the "Maya date. A 
new argument for the structural arrangement used by Morley and myself is found 
in a statement of Juan Pio Perez, in his early article on the Maya calendar, that the 
katuns began on the second day of the Maya year. Now he thought that katuns we § 
24 years in length instead of 7200 days. But the only katun termination that mi eter 
the condition was the last one - be recorded in heathen times, namely: — 
12- 8- 0- 0- 0, 2 Ahau 3 Pop, Aug. 5, 1516 A. D. oe 5 
Hence it seems that some statement concerning this position must once have exi ted. 
Other recent works to which frequent references are made include: ‘ 
S. G. Morley, The Supplementary Series, Holmes Anniversary Volume, Ww S 
ington, 1916. Inscriptions at Copan, Pub. 219, Carnegie Institution of Washingt 
1920. Also “Archeology,” in the Year Book of the Carnegie Institution of 
ington, Nos. 13-26, 1915-27. 
F. Blom and O. G. La Farge, Tribes and Temples, 2 vols. Tulane Ur 
Publication, 1927. 5 


BUFFALO SOCIETY OF NATURAL SCIENCES 7 


Mayas may have observed sidereal as well as synodic revolutions is 
a kind of zodiac consisting of thirteen signs or houses, which was 
surely in existence during the last centuries of their civilization. 


The great problem of calendar makers among all peoples is that 
of intercalation. Perhaps the commonest type of original calendar 
is the luni-solar one. Here the problem is to adjust the apparent 
-movements of the moon and the sun, which give rise to the lunation 
and the tropical year. Most American Indian tribes have calendars 
of this kind and we may assume that the Mayas also had a luni- 
solar calendar at the time they started their day-count. Schemes for 
intercalating entire months are developed by peoples having luni- 
solar calendars and occasionally an effort is also made to find rules 
for distributing 29 day and 30 day months in such a fashion that 
the number of elapsed days can also be recovered. Perhaps the most 
famous scheme of this kind was the one elaborated by the Greek 
astronomer Meton. He found that 19 tropical years and 235 luna- 
tions are very nearly equal to 6940 days and this period of time is 
named the Metonic cycle in his honor.’ 


In other calendars the Moon is neglected and the year is made 
up of 12 formal months of 30 days each plus 5 days, making a total 
of 365 days. In this case the problem of intercalation is simply one 
of inserting enough days as the years go by to overcome the excess 
of the tropical year over the calendar year. Perhaps the most accu- 
rate arrangement to meet this difficulty was reached by Omar Khay- 
yam and other Persian astronomers, but most persons are better 
acquainted with the intercalary schemes of Julius Caesar and Pope 
Gregory. Still another series of calendars, especially those of 
Assyria, India and China, are controlled by zodiacs and these some- 
times yield sidereal years differing from synodic years by the slight 
amount of the precession of the equinox. 


But intercalation is not necessary to good calendar making. The 
months of a calendar not corrected by intercalation are not fixed in 
the year but move slowly around the year. The Arabs have an 
uncorrected calendar of 12 lunations and the months complete the 
round of the seasons in about 33 years. The ancient Egyptians main- 
tained for thousands of years an uncorrected calendar of 365 days, 
the months of which receded much more slowly and made a backward 
round of the season in 1507 years.2 They seem to have thought 
that only 1460 years were necessary to effect this change, being led 
astray by a faulty coordination of the rising of the Nile with the 
heliacal rising of Sothis or Sirius. The Nile floods in accordance 
with the tropical year and Sirius, if we neglect his small proper 


1The period of 6940 days was independently reached by the Chinese and the 
Mayas, neither following the Greek scheme of intercalating months. 

?The Mayas used the equation 1508 calendar years (29 & 52 & 365 = 550420 
== 1507 tropical years, several examples of which will be given as we proceed. 


8 VENUS AND THE MUON 


motion, rises in accordance with the sidereal year which is some 
minutes longer than the cycle of the solstices and equine ig 


It is now pretty generally admitted that the calendar year of 
the Mayas and other civilized nations of Middle America was also 
vague year of 365 days, uncorrected by intercalations, in spite oO 
the fact that the amount of error was very nicely calculated. The 
Maya months therefore receded through the year of nature—and oO 
our own corrected calendar—at a rate corresponding to our leap year 
intercalations. Indeed it is practically certain—and this is the gist of 
the present demonstration—that all the varieties of calendars pow 


places of the Moon, Venus, etc., corresponded with aca ‘ob s 
vations.* aa 


Early students? of the Maya inscriptions made no attempts t 
find historical settings for the Venus and Lunar calendars or even to 
express the Maya dates and designations in the inscriptions and manu- 
scripts in terms of Julian or Gregorian time. They merely examined 
the. various tables as absolute arrangements of mean intervals of 
planetary motions cast in the mould of the Maya day count and its — 
collateral permutations. Professor Robert W. Willson,® late astrono- 
mer at Harvard, was the first to approach the astronomical ae 
as a truly historical problem. He studied various schemes of pee 


1Although the Mayas did not correct their civil calendar they eoame ever: 1 
ways of calculating the correction. For instance they noted that 70 tuns were very © 
close to 69 tropical years (error about 1.37 days). They then found that if they 
took this period three times (210 tuns = 207 years) and dropped a tun from one pee + 
of the equation and a year from the other, that the resulting 209 tuns = 206 tropical 
years was very close indeed. At Chichen there may be two applications of t i 
as follows: sew 

Akab’tcib, Lintel 
11- ey 4 - 12 Ahau 13 Tzec, Mar. 9, 995 A. D.~ 
10- 9- 0- J 
11-12- 0- 0- 0, 8 Ahau 3 Mol, Mar. 9, 1201 A.D. 
Nunnery, Lintels 
11- ees 4 0, 1 Ahau:13Yax, = Jute 22;° (975 eAn: 
10- 9-0. 
11-11- 0- 0- 0, 10 Ahau 3 Mac, June 22, 1181 A. D. . 
The second example is doubtful. . 


*I refer here especially to Ernst Foérstemann whose Commentary on ae ‘pees i 
Codex has been translated in Pap. Peabody Museum, IV, No. 2, pp. 48-266, 1906, and 
to Charles P. Bowditch whose The Numeration, Calendar Systems and Astronomical 
Knowledge of the Mayas appeared in 1910. 


3A posthumous paper Astronomical Dates in the Dresden Codex Pap 
Museum, IV, No. 3, Cambridge, 1924. 


BUFFALO SOCIETY OF NATURAL SCIENCES 9 


cant positions in relation to the Earth and the Sun. Mr. Teeple 
and Mr. Thompson in more recent papers have made the same 
assumption. ah 


In the present thesis the Venus and Lunar calendars are pre- 
sented as formal patterns of mean motions uncorrected from an 
historical time of inauguration. At this time of inauguration the 
calendarial positions coincided with the actual positions but as time 
went on the calendar positions drew away from the actual positions 
in the same manner as the months of a vague year necessarily draw 
away from their original stations. The rate of departure depends, 
of course, on the amount of error in the particular pattern of mean 
motions. 


It will be demonstrated, moreover, that the true positions of 
Venus and the Moon were also noted after divergence had taken 
place, especially when significant phases coincided with round num- 
bers in the day count, with important points in the tropical year 
or with leading positions in the calendars of other planets. Many 
Maya dates have a double or even a triple significance leading us 
to the conclusion that Maya astronomy had its astrological uses. 


THE NATURAL BASIS OF THE VENUS CALENDAR 


The problem which the Mayas solved out of the appearances 
of the planet Venus was vastly different from that of measuring the 
tropical year. The natural cycle of the year, recognized by the most 
barbarous tribes of men, is indicated by changing aspects of nature, 
during the alternation of the seasons, as well as by the swinging of 
the points of sunrise across the east and west line of the equinoxes. 
Also the rising or setting of fixed stars and constellations in certain 
combinations with the Sun can be used by primitive peoples to give 
the length of the year since the year of the stars differs by an 
unappreciated 20 minutes from that of the seasons. 


But Venus is one of several wanderers along the starry road of 
the zodiac and her course is hard to follow. Today with the explana- 
tion of Copernicus and the scientific plotting of orbits we under- 
stand the apparent movements of Venus as viewed from our whirling 
Earth. But we still make poetic use of Lucifer and Hesperus for the 
double life of Venus which the early Greeks thought corresponded 
to distinct heavenly bodies. 


At the beginning of a typical career Venus appears faintly in 
the east just before sunrise, and the point nearest to the Sun where 
she can be seen by the unaided eye is called the heliacal rising. Then 
at increasingly earlier risings she reaches a state of glowing brilliancy 
before the morning dawn. Really at this time Venus is a crescent, 
but so near the Earth that she exposes a larger apparent area of 
illumination than when she is disk-shaped in a distant part of her 


10 VENUS AND THE MOON 


orbit. The luster does not last, for Venus grows smaller and nae 
as she swings on her orbit away from the Earth. Reaching the — 
greatest elongation or apparent distance from the Sun, the planet 
seems to turn again toward that central attraction. There are incon- ~ 
spicuous weeks during which she moves, as a diminishing orb, into _ 
the morning twilight and is lost sight of at heliacal setting as morning 
star. After a considerable disappearance, while passing behind the 
Sun at superior conjunction, Venus emerges in the evening twilight 
as a faint and far away luminary closely following the Sun down 
into the west. On successive nights Venus is higher and higher in 
the sky when first glimpsed after sunset. Slowly her fire kindles and 

she gradually becomes a brilliant spectacle standing above the ruddy ~ 
bar of fallen day. Her change in motion among the stars, marked by 
her appearing to stand still and then to move backward, is an effect 
of relativity as regards the moving Earth, which Venus rapidly 
approaches at this part of her career. Her orbit carries her between 
the Earth and the Sun at inferior conjunction and she seems to 
plunge into the sunlight at heliacal setting as evening star. About 
eight days later, under the most favorable conditions, keen eyes see — 
the morning star return to repeat the strange cycle of changes. _ 


If the orbits of Venus and the Earth were perfect circles with 
the Sun at the center, and if Venus made 13 revolutions around the _ 
Sun in exactly the same time that the Earth made 8 revolutions of __ 
precisely 365 days each, the conditions of the Venus calendar of 
the Mayas would be realized in the heavens. Venus would then __ 
pass the Earth every one and three-fifths revolutions of the latter. — 
Compressed in a circle, the possible points of inferior conjunction — 
(when Venus is exactly in line between the Earth and the Sun) © 
would be one-fifth of the circumference of a circle or 72 degrees — 
apart and compressed in a year (although really distributed 584 
days apart over 8 years) the possible dates of inferior conjunction 
would be one-fifth of 365 days, or 73 days, apart. ce 


But the orbits of Venus and the Earth are both elliptical rite ae 
than circular, with that of the Earth having at the present time, 
more than twice the eccentricity of the orbit of Venus. Moreover __ 
the Sun is situated at a focal point of each elliptical orbit and the 
speed of each planet varies according to Keppler’s law. Venus — : 
travels at a more even rate than the Earth each, however, moving ° re 
fastest when nearest the Sun and slowest when most distant. Venus 
gains least on the Earth in December and January with the. result 
that an apparent revolution of the planet covering two winters and 
one summer may consume slightly more than 388 days while one 
falling in the opposite order may take slightly less than 580 days. Pe 
The epee revolutions, which are essentially laps pari on pay Bei 


BUFFALO SOCIETY OF NATURAL SCIENCES Ly 


risings of the planet as morning star, about four days after inferior 
conjunction. This gives a period of obscuration of the planet between 
heliacal setting as evening star and heliacal rising as morning star of 
8 days which is a practical minimum explained by the short twilight 
of the tropics where the Sun sets vertically. On the other hand the 
Mayas allowed 90 days for the obscuration at superior conjunction 
when the planet was in her least interesting phases. 


How THE Mayas FORMALIZED THE VENUS EPHEMERIS 


The Venus calendar of the Dresden Codex, pages 46 to 50 of 
Forstemann’s numbering, to which page 24 is introductory, is a 
permutation of the 260 days of the tzolkin in combination with 
the 365 days of the haab or civil year, and the 584 days of the 
average synodical revolution of Venus. The pattern of intervals is 
repeated three times with identical days but different month posi- 
tions. This table is an outgrowth of the observed correspondence 
between 8 years and 93 revolutions of Venus when the years are 
counted as 365 days, although really about 365.24 days and the 
Venus revolutions at 584 days, although averaging 583.92 days. 
The complete permutation is 65 K 584==104 & 365 = 146 X 260 
= 37,960 days. With an intercalation system it would be necessary 
to interpolate 25 days into the annual calendar to overcome the 
shortage in the formal year and in the case of the Venus calendar 
it would be necessary to intercalate about thirty days. Or if the 
uncorrected annual calendar were the base on which the correction 
of the Venus calendar had to be calculated, an excision of five days 
would be required over the permutation cycle, in accordance with 
the following: 


AES osc snrneennnecennsshraienemnnriveionrsven 37,985 days 


ES ESS 7 i ena enn eae S700. 2 
65 synodical revolutions Of Venus....ccecseeesen TLS ae 


But the Mayas did not make intercalations to keep their annual 
calendar in accord with the seasons nor did they make excisions in 
their Venus calendar to make it agree in turn. Both the annual and 
the Venus calendars started flush with the celestial record at the 
time of their historical inauguration and both moved as purely 
formal patterns across the numbered days of the Long Count and 
the revolving designations of the tzolkin. Also the Lunar calendar 
and in all probability the formal cycles based on Mars, Jupiter, 
Mercury and Saturn were uncorrected by actual intercalations and 
excisions. But methods were devised in each case, as has been said, 
whereby the actual positions of the heavenly bodies could be recov- 
ered from the formal record, or new starts made from historical 
positions which did not involve the principal of intercalation. 


In the Venus table of the Dresden Codex a typical 584 day 
period has the following four divisions representing appearances as 


12 VENUS AND THE MOON 


morning and evening star and the superior and inferior conjunction. ‘ 
When the table departs from 18 Kayab as zero and advances in 
groups of 236, 90, 250 and 8 days, the calculation reaches 9 Z " 
19 Muan, 4 Var aad 12 Yax respectively, as is seen in the following 
arrangement. on ena =A, Baath 

ve a 


ra eS yt 


NATURAL DIVISIONS OF ONE SYNODICAL REVOLUTION. OF Venus 


As formalized in the Venus Calendar Ws 
0 days 18 Kayab Heliacal Rising as ers Sep pet gee 


236 days Duration of Morning Star _ oe 
PEG a as 9 Zac -Heliacal Setting as Morning Star = 
90 “ Invisibility at Superior Conjunction 
326 > 79:19 -Muan Heliacal Rising as Evening Star 
250 ‘“* Duration of Evening Star 


576553 4 Yax Heliacal Setting as Evening Star 
8 ‘“ Invisibility at Inferior Conjunction 

BBA vo2 hake, hat Heliacal Rising as Morning Star As oe 
When the intervals 236, 90, 250 and 8 days, as given abov he Sep 

are repeated five times a return is made to the month positions 
18 Kayab, 9 Zac, 19 Muan, 4 Yax and 12 Yax. This is becaus 
5 xX 584=8 X 365, and 8X 365 from any month position in the 
Maya uncorrected year recovers the same position. Also it will be 


the first one ends: this being an application of the Maya principle 
of the zero of completion. & 


TyPICAL PATTERN OF MONTH PosITIONS = 


For one 8-year Period of the Venus Calendar 


0 days 18 Kayab 0 days Heliacal Rising—Period Begins 
2367 ge 9 Zac ZAG yd ara 
326-92 3 19 Mian 90.=s | i 
5166 4 Yax Pip Vier Heliacal Setting Aes 
FSA Ce ad 27 vax aes Heliacal Rising, 2nd Rev. Begin 
S20ino 3 Zotz 256224 Sats 
910: 27s °713., Mol OD i254 ; 

1 GOs a) eed Be IG ATi a Heliacal Setting ene 
UGS: 6 Zip 8 “  Heliacal Rising, 3rd. Rev. Beg 
1404505" 2 Pax 236 ee Ain 
1494“ 7 Pop ODe ae 

‘WE, Y Cena Geeitamy: Wi ia C= ZI ee Heliacal Setting i, 
17528 5 Kankin ae | Heliacal Rising, 4th Rev 
1088 “| 160 Yaxkin,. 7 23660 Sea 
2078. 6 Ceh op | al 
21260 sows 11 L50 Heliacal Setting ee 
596s elo a ee Heliacal Rising, 5th Rev. 
S592 eee Se itr oo oe eae : ete 
2662-05 0 Tzec ID 

9910 - Oe ea aval cout Heliacal Setting 

29204 Sas abn Sie Heliacal Rising—Period | End ; 


Vey ee ¥ q ’ Ped ' 
ory a po ie 


BUFFALO SOCIETY OF NATURAL SCIENCES 13 


from the month 18 Kayab is made also to depart from a day 1 Ahau 
occupying that position, the intervals of 236, 90, 250 and 8 days are 
found to lead to the following positions in the tzolkin counting from 
1 Ahau: 


PATTERN OF DaysS IN AN 8-YEAR PERIOD OF THE VENUS CALENDAR 


First Venus Rev.+236= 3Cib +90= 2Cimi +250=5 Cib +8—13 Kan 


Second ** * +236= 2 Ahau +90=—= 10c -+250=4 Ahau +812 Lamat 
Tbicd>. “* “ +236= 1Kan +9013 Ix +250=3 Kan +811 Eb 
Fourth “ “ +236=13 Lamat+90—12 Eznab +2502 Lamat+8=10 Cib 
Fifth 24 Y =1-236=-12 Eb +90= 9Ik +250=1 Eb +8= 9 Ahau 


The next series of tzolkin positions count from 9 Ahau with which 
this layout ends: the same days are reached but with different 
coefhcients and the permutation does not exhaust itself until 13 
changes have been run through, making the round of Venus calendar 
equal 65 & 584 or 104 & 365 or 37,960 days. 


The Venus table of the Dresden Codex is shown on five pages. 
The upper half of each page is given over to a picture with a block 
of hieroglyphs above and preceded by four columns of day signs 
which are intended to be read in rows across the five pages. Each 
column consists of 13 repetitions of the same day sign but with 
varying numerical coefficients, and the table as a whole exhausts the 
104-year permutation cycle explained above. The last glyph in the 
last column of the fifth page is 1 Ahau which is the end or culmina- 
tion of the table and which also must be imagined as the concealed 
beginning. 


The lower half of each page has two more pictures on the right 
hand side arranged directly under the top picture and each explained 
by a block of hieroglyphs. These two pictures are supposed to repre- 
sent the gods which preside over the five Venus years, the middle 
pictures are warring gods and the bottom pictures are gods which 
have been “killed.” In other words an astrological pattern is involved 
which we find reflected in various codices of southern Mexico.* 


On the left hand side of the lower half of each page we find a 
block of four columns of five glyphs. The top row in each case 
consists of month signs, the second row consists of zero or completion 
signs, the third row of hieroglyphs of the cardinal points, the fourth 
row of the symbols of gods, etc., differing in each case, while the 
fifth and bottom row consists of Venus symbols. Under this passage 
are numbers which furnish a cumulative account of the Venus 
intervals beginning with 236 and ending on the fifth page with 2920. 


The bottom glyph blocks consist of 4 columns of 5 or 6 glyphs 
each. The first row and last are two series of month signs; other 
rows give the hieroglyphs of gods, the symbols of the four directions, 


1See E. Seler Die Venusperiode in den Bilderschriften der Codex Borgia-Gruppe 
in Gesam Abh. I, pp. 618-667. Berlin, 1902. 


14 VENUS AND THE MOUN 


etc. Finally at the bottom in red numerals we find the numbers 
236, 90, 250 and 8 repeated on each page. 


The three rows of month signs are three locations for the day 
signs, or three Venus calendars departing from the following posi- 
tions, Top row, 1 Ahau 13 Mac; Middle row, 1 Ahau 18 Kayab; 
Lower row, 1 Ahau 3 Xul. I believe the middle row is the Venus 
calendar, par excellence, and in the following table call it Calendar A. 
The top row I call Calendar B and the lower one Calendar C. Before 
going into further analysis I put the complete pattern of month 
positions before the reader: 


MONTH POosITIONS IN VENUS TABLE—DRESDEN CODEX . 


Terminal Dates of Divisions in Formal Synodic Revolutions 
Corresponding to Heliacal Risings and Settings of Venus 


Morning Star 


Superior Conj. 


Evening Star 


Inferior Conj. 


236 days 90 days 250 days » 8 days 

Hel. Setting I Hel. Rising II Hel. Setting II Hel. Rising I 
Page 46 
B 4 Yaxkin 14 Zac 19 Tzec 7 Xul 
A 8 Zac 18 Muan 4 Yax 12 Yax 
C 19 Kayab 4 Zotz 14 Pax 2 Kayab 
Page 47 
B 3 Cumhu 8 Zotz 18 Pax 6 Kayab 
A 3 Zotz, 13 Mol 18 Uo 6 Zip 
C 13 Yax 3 Muan 8 Chen 16 Chen 
Page 48 
B 19: Yox 7 Muan 12 Chen 0 Yax 
A 2 Muan 7 Pop 17 Mac 5 Kankin 
C 7 Zip 17 Yaxkin 2 Uo 10 Uo 
Page 49 
B 11 Zip 1 Mol 6 Uo 14 Uo 
A 16 Yaxkin 6 Ceh 11 Xul 19 Xul 
C 6 Kankin 16 Cumhu 1 Mac 9 Mac 
Page 50 
B 10 Kankin 0 Uayeb 5 Mac 13 Mac* 
A 15 Cumhu 0 Tzec 10 Kayab 18 Kayab* 
C 0 Xul 10 Zac 15 Tzec 3 Xul* 


*These are the final dates which must also be regarded as the suppressed 
beginning dates. 


PLACING THE VENUS TABLES IN ACTUAL CHRONOLOGY 


The Dresden Codex, although reflecting the science of astronomy 
developed during the brilliant First Empire of the Mayas, is itself 
a product of later time. Since, however, it fails to exhibit the fea- 
tures in art and ceremony introduced into Yucatan by the Toltecs, 
we may date its original compilation before 1200 A. D., or at the 
latest, shortly after this date. Perhaps Calendar B is intended to be 
used contemporaneously. The latest date in the Dresden Codex, 
clearly stated by the Long Count method, is 10-19- 6- 1- 8, 12 Lamat 
6 Cumhu, November 28, 950 A. D. from which an indicated sub- 
traction of 8 days is made, leading to the date 10-19- 6- 1- 0, 4 Ahau 


sw 


BUFFALO SOCIETY OF NATURAL SCIENCES 15 


18 Kayab, November 20, 950 A.D.1 This date coincides exactly 
with an heliacal rising of Venus as morning star? four days after 
inferior conjunction with the Sun on Julian Day 2,068,360. 


From this contact Calendar A, beginning with 1 Ahau 18 Kayab, 
can be restored as follows: 
10-18- 9-15- 0, 1 Ahau 18 Kayab, Nov. 24, 934 A.D. 


Maya Day 1,573,140 = Julian Day 2,062,524 
Inferior conjunction of Venus, J. D. DOG ike? 


Calendar B has its setting in history as follows: 


11-13- 6-12- 0, 1 Ahau 13 Mac. mes et 2272 AR: 
Maya Day 1,680,000 = Julian Day 2,169,384 
Inferior conjunction of Venus, J. D. 2,169,377.5 
Here the adjustment may seem at first glance somewhat defective, 
but note the fact that the Maya day is a round number in the decimal 
system and that the summer solstice is reached. Other points in 
regard to this position will receive later comment. 


Calendar C in the following historic location gives an exact 
coincidence with inferior. conjunction for about the same epoch as 


Calendar B. 


11-13- O- 3- 0, 1 Ahau 3 Xul, LP Tee 0-8 Ik UW ee BF 
Maya Day 1,677,660 = Julian Day 2,167,044 
Inferior conjunction of Venus, J. D. 2,167,044.5 


One Venus round earlier (104 & 365 days) will find the planet still 
in the phase of evening star, 6 days before inferior conjunction (J. D. 
2,129,090.2) and therefore very close to heliacal setting, while a 
Venus round later the planet is morning star 5 days after inferior 
conjunction as follows: 


11-13- 0- 3- 0, tc Ahau 3 Xuk Jane ostrich Ds 
5- 5- 8- O 

11-18- 5-11- 0, Li Abas 323i. Dec 2921324 Awd. 

Maya Day 1,715,620 = Julian Day 2,205,004 

Inferior conjunction of Venus, J. D. 2,204,998.7 


I also give at this time the historical location of a Venus calendar 
departing from a fourth date, 1 Ahau 18 Uo, emphasized on page 24 
of the Dresden Codex, the preface to the Venus table: here the 
coincidence is perfect since the date reached for the heliacal rising is 
exactly 4 days after the inferior conjunction of Venus with the Sun. 


£12 8-.7-13- 0; 1 Ahau 18 Us Decw2e tio Axa. 
Maya Day 1,645,380 = Julian Day 2,133,764 
Inferior conjunction of Venus, J. D. 2,133,760.1 


This date is found in the preamble to the Lunar table but is doubtless a cross 
reference to Venus even as we shall see cross references to the Moon in the preamble 
of the Venus Table. 


2IT calculate the heliacal risings from data in a ms. Dates of the Inferior Con- 
functions of Venus 181 A. D. to 1527 A. D. by R. W. Willson. 


16 VENUS AND THE MOON 


REFERENCES TO VENUS IN ANCIENT INSCRIPTIONS 


It might be argued, if the Dresden Codex were the only source 
of information concerning the Venus calendar that this was a late 
invention. But references to Venus are also found in the ancient 
inscriptions. Indeed there are several categories of references and I 
therefore begin with a few statements which seem beyond cavil. 


On Block 6 of the Hieroglyphic Stairway at Naranjo we see 


the date 7 Akbal 16 Muan, at the top of the block (Glyphs B 
and Cl), which is tied by a distance number, in Glyph B3, to a 
second date, 1 Ahau 8 Kayab, in Glyph C3. At the right of the 


Fo a (esas PASSAGE ON THE HIEROGLYPHIC STAIRWAY AT 
NARANJO. 


The first date falls on an heliacal rising of Venus and following it comes a 
symbol of Venus over that of the Ceremonial New Fire. In the lower section a 
distance number reaches a second date that is a round number. 


first date is a very clear Venus sign, of the same type as those of the 
Dresden Codex, over a symbol which I have elsewhere discussed as 
a sacred fire bundle.*| In the Long Count these dates are placed as 
follows: 


9- 9-18-16 3, 7 Akbal 16 Muan, Feb. 26, 372 A.D. 
pes Fe Ie 
9-10- 0 0O- 0, 1 Ahauw 8 Kayab;> Mar. 3080 373 ee 


1See Reduction of Mayan Dates, p. 202. 


4 Cee 


BUFFALO SOCIETY OF NATURAL SCIENCES 17 


The first of these dates, to which the Venus symbol is attached, 
equals Maya Day 1,367,603 and adding 489,384, the constant differ- 
ence between the Maya Day and the Julian Day, we get 1,856,987 
and are gratified to find that an inferior conjunction of Venus with 
the Sun took place on J. D. 1,856,983.0 so that the Maya statement 
undoubtedly refers to the heliacal rising of Venus 4 days after 
inferior conjunction in accordance with the allowance of the Dresden 
Codex. Perhaps a new ceremonial fire was lighted on this occasion. 


We find a similar ceremonial fire recorded on Stela 23 at Naranjo 
in connection with the date 6 Ahau 13 Muan which is declared to 
be the end of Katun 14. This is: 


9-14- 0- 0- 0, 6 Ahau 13 Muan, Feb.) 45 6452.AD:; 


This number reduces to J. D. 1,886,184 and we find that an inferior 
conjunction of Venus took place five days before on J. D. 1,886,179. 
In other words here was an heliacal rising of Venus coinciding with 
the terminal day of a major round number in the day count. Now 
there is no Venus symbol of the type known from the Dresden 
Codex in the passage we have just examined but if we turn to 
Stela C at Copan, where the same katun ending is declared, we do 
find a clear case of the usual Venus sign. In connection with this 
symbol we get the following remarkable subtraction: 

Rie e007 0  .6° Ahau 13. Muan,.' 3) Feb, ~ 4,/ 2452 AD: 

Bre 4- <5 1-0 

10-19-14-17- 0, 6 Ahau 18 Kayab, Apr. 12, 4165 B.C. 
The true inwardness of this subtraction into the distant past does 
not. appear until we consider the Moon. But it will be seen that 
the month position 18 Kayab, emphasized in the Dresden Codex 
is recorded here and that it falls on April 12 in the natural year. 
Now it happens that on page 24 of the Dresden Codex, the page 
that by proper numbering should come just before the Venus table 
of pages 46-50, that the following date is recorded: 


9- 9 9-16- 0, 1 Ahau 18 Kayab, April 12, 363 A.D. 


It will be observed that we have here a combination of the Maya 
month position 18 Kayab and the Gregorian position April 12 just 
as in the distant date on Stela C at Copan. Again we must post- 
pone for the moment our explanation and return to another clear 
example of the Venus symbol in combination with an accurately 
recorded position in the Maya Long Count. 


On Stela 12 at Uaxactun 1 Ahau 3 Yaxkin is recorded in com- 
bination with the two forms of the Venus glyph found in the 
Dresden Codex. This date is the end of a katun, namely: 


1029-02707 0.. Si iAhad:.3 WYasxkin« p fully: 6; 2629 AR D; 
Maya Day 1,461,600 = Julian Day 1,950,984. 


An inferior conjunction of Venus took place about five days after 


18 VENUS AND THE MOON 


this point in time, which therefore practically coincides with the 
heliacal setting of Venus as evening star. 


ROUND NUMBERS THAT COINCIDE WITH APPEARANCES OF VENUS 


It will be remembered that we already have had Venus records 
in connection with two katun endings during the period of the First 
Empire. Scrutinizing the likelihood of such coincidences we are sur- 


Fic. 2. INSCRIPTION ON STELA 12 AT UAXACTUN. 


A round number in the Day Count which coincides with the heliacal setting 
_of Venus. 


prized to find that the interval of 3 katuns (21,600 days) is only 
five days less than the mean value for 37 synodical revolutions of 
Venus (21,605.04 days). Practically the interval fluctuates some- 
what either way from this mean but the following close corre- 
spondences are noted with others less close preceding and following 
at intervals of 3 katuns. : 


9-Lle 0- 0° 0, 12 Ahan 8 *Gehe Dec. 15, 3924 
Maya Day 1,375,200 = Julian Day 1,864,584 
Inferior conjunction of Venus, Julian Day 1,864,572.6 


9-14- 0- 0- 0, 6 Ahau 13 Muan, Feb: -.4, > 432522 
Maya Day 1,396,800 = Julian Day ~ 1,886,184 
Inferior conjunction of Venus, Julian Day  1,886,179.0 


9-17- O- O- 0, 13 Ahau 18 Cumhu, Mar. 27, 511 A.D. 
Maya Day 1,418,400 = Julian Day 1,907,784 
Inferior conjunction of Venus, Julian Day 1,907,783.6 


10- 0-:0-.0- 0; “7 Ahau’ 48 Zip: May 17, ‘S70°AG Dy 
Maya Day 1,440,000 = Julian Day 1,929,384 
Inferior conjunction of Venus, Julian Day 1,929,386.9 


10- 3- 0- O- O, 1 Ahau- 3 Yaxkin, July” 6; (629%Am 
Maya Day 1,461,600 = Julian Day 1,950,984 
Inferior conjunction of Venus, Julian Day 1,950,990.3 


BUFFALO SOCIETY OF NATURAL SCIENCES 19 


THE INAUGURATION OF THE VENUS CALENDAR 


These dates greatly enlarge our comparisons, but before going 
farther into the matter of the ancient records the inauguration of the 
Venus calendar calls for some attention. The Dresden Codex gives 
evidence concerning the operation of the peculiar time count from 
the Tenth to the Thirteenth centuries of the Christian era and the 
inscriptions on monuments of the First Empire give evidence of 
observances from the First to the Seventh centuries. But the inaugu- 
ration seems to have occurred during the Sixth century before Christ. 


I have elsewhere shown that the actual counting of days by the 
Mayas began on August 6, 613 B. C.1 and that the civil calendar was 
inaugurated about 580 B.C. when 0 Pop, the astronomical new year 
day, coincided with the winter solstice and 0 Yaxkin, the farmer’s 
new year day, fell on April 21. The celestial register had already 
covered in excess of 12,000 days, enabling the great astronomer who 
invented the Maya time count to formulate the year at 365 days. 
He may have observed that a bright star made its first appearance in 
the east just before sunrise five different times during a term of 8 
years, once in pretty close adjustment with the farmer’s new year. 
It would, however, have taken a life time or more to check and 
recheck the phenomena and reduce the somewhat variable data to 
a calendarial pattern. The heavy emphasis placed on April 12, 
November 17, the summer solstice, etc., in combination with the 
Maya month positions 19 Xul, 18 Kayab, 12 Yax, etc., leads one 
to place the inauguration of this special planetary calendar between 
540 and 530 B.C. I give in A of the following table a set of eight 
heliacal risings of Venus, calculated at 4 days after inferior conjunc- 
tion,” and in B the necessary warping to comply with the formalities 
of the calendar. Only 5 of these heliacal risings are necessary to 
form a minor round. 


ORIGINAL SETTING OF THE VENUS CALENDAR 


A. Heliacal Risings of Venus. 


7- 3-12-13- 4, 12 Kan TeV axkin se Apiiks 20 4b 
1-11- 2 (582.4 days) 


Peal 4s) GeG.  'O Cimi- 19) Kayab Novel iia 34005 
111-3 (583.1 days) 

Teualoclas Se} Mulue.12 “Yax June 2357-338) - 
l-11- 7 (586.6 days) 

7 3-17-10-16, 9 Cib 9 Zip lane -30e eae 


1-11- 0 (580.1 days) 


1This is the round number written 7-0-0-0-0, 10 Ahau 18 Zac; the Mundane era 
of October 14, 3373 B. C. was reached by counting back 7 baktuns to a zero date 
written 13-0-0-0-0, 4 Ahau 8 Cumhu. The third Maya era, that of the Chronicles, 
so-called, departs from 9-0-0-0-0, 8 Ahau 13 Ceh, February 10, 176 A. D. 


2J reach these dates by a specially constructed Venus table based on coincidence 
of a Venus phase and the same point in the tropical year (error about iM mn 0) 
251 years. 


20 VENUS AND THE MOON he, 


Te 9:19- 3-16, 4 Cib 4 Kankin Sept 2) 33 5en ame 


6 
1-ll- 8 (587.4 days) ie. 
72 Be OAS 4. 7 Kean 2. Yaxkin” Apr. 13; 533) 
bei te 2 (582.2 days) PRE ISS 
7- 4- 2- 8 6 4 Cimi 19 Kayab Nov. 149,) “93 ee : 
1-1l- 3 (583.3 days) 
9 


yee aE ia 2 Muluc 12 Yax June 21,7) 300m 


B. Calendarial Positions of Venus. bees 
Teese 3713201; 9 Imix 19 Xul Ape 12, v4] B.C, , 


l-1ll- 4 (584 days) . ' 
7- 3-14- 6 5, 8 Chicchan 18 Kayab Nov. 16, 540 ~ 


l-1l- 4 (584 days) ‘ec = 
7-'3-15-17- 9, 7. Mule 12 Yax.” June 23,730 eee 
l-ll- 4 (584 days) 
- 3-17-10-13, 6 Ben 6 Zip . ‘Jan. 928555 26eee 


‘! 
l-1l- 4 (584 days) 
72 3-19- 3-17, ~ 5 Caban ) Kankin Sept: °3,.25a3ee 
1-l1- 4° (584 days) 
1- 4 O-15- 
i) 


1 4 Imix 19 Xul © Apri: 10; 3.23ee 

1-1l- 4 (584 days) Ea 

- 4¢ 2- 8- 5, 3 Chicchan 18 Kayab Nov. 14, 332557 
l-ll- 4 (584 days) 


4 4¢ 4e 1-9, 2 Mulue ~ 12° Yax June. 2 ee 


Common foci must be found for positions in the tropical year 
(as expressed in the backward projection of our Gregorian calendar), 


the actual days when Venus rose in proximity to the Sun as morning 
star. The exigencies give, after all, little leeway. Three movements = = = 
made at different rates must be carried back till all are even, - Now 2) ae 
the natural year advances in a cycle of 365.24 days, while the Maya _ ‘s 
year advances in a cycle of 365 days and Venus at a rate that 
reduces to 364.95 days. In 243, or better yet 251 years, the phases 
of Venus return to the same times in the tropical year. Thus if | 
April 12 serves to mark a significant phase of the planet in 541 B. C., 
the same phase will repeat on April 12, 290 B. C.; ; April 12,39 B.C; 
April 12,- 2120A; Desetemae ine adjustment is not quite perfect b 
is near enough for general purposes. In this interval of 251 years” 
Venus recedes about 12 days in the Maya year and the Maya year a 
recedes about 61 days in the tropical year. The coincidence can no 
iceer take place on 19 Xul but instead on 7 Xul and this 7 X 
; located 73 days, or one-fifth of a year in recession. from t 
fee status of 19 Xul. 


signs in the Venus calendar of the Dresden Codex are as follows fe 
the phase of heliacal rising: Deh o. 


Calendar A 12 Yax, 6 Zip, 5 Kankin, 19 Xul, 18 ene cat 
CalendarB 7Xul, 6Kayab, 0 Yax, 14 Uo, 13 Mace ae DS 


In 251 years, or 157 synodic revolutions of Venus, the month lis 
are run over 31 times plus two additional revolutions. When, the 


BUFFALO SOCIETY OF NATURAL SCIENCES 21 


fore, the positions of Calendar B are shifted forward these two extra 
revolutions we have an arrangement not disturbing the sequence 
but disclosing the difference of 12 days which is the essential reces- 
sion of the appearances of the planet, in terms of the Maya year, 
for an interval of 251 years; thus: 


Calendar A. 12 Yax, - 6 Zip; 5 Kankin, 19 Xul, 18 Kayab. 
Calendar B G2 ax 1 45bioy 13 Mac, 7 Xul, 6 Kayab. 


That Calendar B of the Dresden Codex restores the allignment 
between the Maya year and the actual positions of Venus after 
Calendar A has been in operation for about two and a half centuries 
may be seen from an examination of the historical positions given 
above. The search for a special day, 1 Ahau, limited the choice of 
beginnings to 1 Ahau 18 Kayab for Calendar A and 1 Ahau 13 Mac 
for Calendar B and slightly distorted the adjustment from its maxi- 
mum accuracy. The normal succession might be better expressed by 
adding the interval in the following fashion: 


10-19- 6- 1- 0, 4 Ahau 18 Kayab, Nov.20, 950 A.D. Heliacal Rising of 


12-14-11-17 Venus 
iehr0-12-17,. 4 Cib > 14 Uo, Nov. 20,1201 A.D. Heliacal Rising of 
Venus 


If the system indicated in these two calendars is carried to its 
logical conclusion the original month positions of Calendar A are 
recovered in 6 X 251— 1506 years. This is just a year less than 
the major cycle of the Maya civil year in which 29 calendar rounds 
or 1508 civil years are found to equal 1507 tropical years. In other 
words if Venus appeared as morning star on 19 Xul and April 12 
in 541 B.C. she would appear, according to rule, again on 19 Xul 
and April 12, 1506 years later, thus: 


Actual 
Heliacal Risings by Calendar Julian Days Inf. Conj. 
7312-13-11. 9 Imix 19 Xul, Apr. 12,541 B.C, J.D.1,523,565, 1,323,364.3 
3-15- 8-17- 0, (29 calendar rounds) 550,420 
11- O- 1-12- 1, 9 Imix 19 Xul, Apr. 12,966 A.D. J.D. 2,073,985 
1- O- 5, (1 civil year) 365 


11- 0- 0-11-16, 8 Cib 19 Xul, Apr. 12, 965 A.D. J.D. 2,073,620 2,073,616.9 


The time required for 942 synodical revolutions of Venus is 
550,052.6 days or about two days over the calendarial allowance. 


The full pattern of the Venus calendar is embodied in the 
following table: and it will be noted that the recovery of Calendar A 
after Calendar F is made by allowing a recession of 13 instead of 
12 days for the last offset. 


TABLE SHOWING OFFSETS OF THE VENUS CALENDAR 


Aproid Nov. 16 June 23 Jan. 28 Sept. 3 
A 19 Xul 18 Kayab Lonyax 6 Zip 5 Kankin 
B 0 Yax 14 Uo 13 Mac 7 Xul 6 Kayab 


C 1 Mac 15 Tzec 14 Pax 8 Chen 2 Uo 


ee VENUS AND THE MOON 


2-Pax 16 Mol 10 Pop 9 Ceh 3 Tec 


D 

E 3 Uayeb 17 Zac 11 Zotz 10 Muan 4 Mol © ah 
F 19 Zip 18 Kankin 12 Yaxkin 11 Cumhu pet rider im. 
A 19 Xul - 18 Kayab 12 ¥ax 6 Zip 5 Kankin 


The use of a complete cycle of 1506 years may be inferred from 
the important date in the Lunar table which places Calendar A in 
its proper historical setting. But there is no evidence that Calendar A 
was ever really supplanted except for purposes of easy calculation. — Le 
The only month positions in the Maya year that seem to have a 
ceremonial significance in what may be called the Venus cult are 
19 Xul, 18 Kayab, 12 Yax, 6 Zip and 5 Kankin or the nearest posi- — 
tions to these which can be occupied by round numbers. Since 
18 Kayab is the only one that can be occupied by a round sata 2 ie 
it becomes the outstanding date. The important approximations are 
18 Xul, 13 Yax, 3 or 8 Zip and 3 or 8 Kankin. 


HIEROGLYPHS OF VENUS 


There are several hieroglyphs of the planet Venus perhaps _ ¢ 
representing different aspects. Two forms common to the inscrip- a 


(2) ) BE Oe 
He WEY (f 
ay [2 : ed) \Yo 


Fic. 3. VENUS GLYPHS. 


First line: simple Venus glyphs. Second, third and fourth lines: Venus titles 
in the introducing glyphs of Initial Series. 


The first of these ea symbols of Venus may be deacr heat as” 
pair of circles held in an ornamental bracket. The second one seem 
in some cases, merely to be the first symbol doubled over on ae 
It consists of four circles arranged in a rectangle, aes there is. a 


against the notch in the second. 


BUFFALO SOCIETY OF NATURAL SCIENCES 23 


Lamat was, par excellence, the day of Venus, why, I am not 
able to say. The hieroglyph of this day is generally a somewhat 
specialized type of the second Venus symbol, but on occasion the 
first sign of Venus is used, or even a grotesque face, also representing 
the planet. This face, not previously recognized as a hieroglyph of 
Venus, belongs to a creature which I have ventured to call the 
Venus Monster. It is the front head of the grotesque double-headed 
creature to which Maudslay gave the name Two-Headed Dragon. 
This front head of the Two-Headed Dragon contains the Venus 
symbol in the eye or prominently attached to the ear ornament. 
I have elsewhere examined the symbolism of the Two-Headed Dragon 
(A Study of Mayan Art, pp. 53-56) and suggested that it was 
related in some fashion to calamities of flood and drought. It now 
appears that these calamities were awaited with dread at the times 
of the eight day obscuration of Venus at inferior conjunction with 
the Sun. The rear head of the double monster carries the Sun symbol 
and the front head carries the Venus symbol. Bones and other signs 
of death are applied to the heads as well as streams of water and the 
elongated body is sometimes converted into a band of celestial symbols 
possibly intended to represent the firmament. 


Among the hieroglyphs for Venus which I have been able to 
recognize through repeated association with dates of Venus signifi- 
cance is a cartouche with five dots, one in the center and one near 


OLY 


Fic. 4. PASSAGE ON LINTEL 4 AT PIEDRAS NEGRAS. 


Date of Venus coincidence in combination with two other significant dates. 


each of the four rounded corners. These five dots probably refer to 
the five Venus revolutions of an eight year period. Sometimes the 
Venus Monster wears these five dots on his forehead. Also the 
double type of Venus hieroglyph in the codices and the Lamat 
variation embody the idea of five markings, one being in the center 
while the others are ranged about it in a rectangular formation. 
Sometimes this last Wenus symbol is combined with the kin or sun 
sign in a device that may represent the conjunction of Venus with 


the Sun. 


24 VENUS AND THE MOON ~ 


OTHER REFERENCES TO VENUS IN ANCIENT INSCRIPTIONS 


It is now possible to give a series of other references to Venus 
in which these newly-recognized hieroglyphs are used. The glyph 
with the five dots is found in connection with the final passage on 
Lintel 4 of Piedras Negras which I render as follows: 


9-10- 5- 6-10, 7 Oc 8 Zotz, July. 12; 378ese 
13-11 

9-10- 6 2- 1, 5 [mix 19 Kayab, Apr. -9, 3/9 aa 
19-17- 7 

9-1l- 6 1- 8, 3 Lamat 6 Chen, Oct. 13, 398 Ae) 


Here the first date coincides with an inferior conjunction of Venus 
on J. D. 1,859,314.7, the second reaches April 9 of the astronomical 
base line at Copan and the last is a true anniversary of the Mundane 
era. Perhaps also there are lunar conformities. 


Stela A at Copan. The Initial Series of Stela A at Copan 
exactly records the day of an inferior conjunction of Venus and the 
text contains Venus glyphs. This important inscription can be 
written as follows: 


9-14-19- 8- 0, 12 Ahau 18 Cumhu, Apr. 5, 471 A.D. 
3- 0 subtract ; 
9-14-19- 5- 0, 4 Ahau 18 Muan, Feb. 4; 471 -AL 
ee yee 
9-15- 0- O- O, 4 Ahau 13 Yax, Oct. 2235 47 Pa ie 
oe PR ee 
9-15- 0-93- 0; 12 Ahau 13 Mae, Dec. 21, “4713 A2Ds 


Here the first date is the conjunction of Venus on Julian Day, 
1,893,185.2 and from it additional statements can be drawn. First, 
April 5 is the original date reached by the astronomical base line at 
Copan, April 9, the date of the heliacal rising after the recorded 
conjunction, is the second setting of the base line, while 0 Pop; the 
Maya new year day, follows in three days on April 12, the last and 
present setting of the base line, and a date, moreover, that is espe- 
cially emphasized in relation to Venus. The inscription of Stela A 
must be considered in relation to several others. The subtraction of 
3 uinals to reach 4 Ahau 18 Muan on February 4 gives a date also 
important on Stela C and Altar U. It is one Metonic cycle after 
the Venus coincidence on 9-14- 0- 0- 0, 6 Ahau 13 Muan, Feb- 
ruary 4, 452 A.D. The date 9-15- 0- 0- 0, 4 Ahau 13 Yax, has 
Venus significance because 13 Yax is an approximation of 12 Yax 
of the original Venus calendar, while 12 Ahau 13 Mac is the winter 
solstice. 


Venus Calculations at Yaxchilan. Lintel 29 in Structure 10 at 
Yaxchilan has a very clear Venus sign in the introducing glyph of 
an Initial Series that renders 9-13-17-12-10, 8 Oc 13 Yax, October 


BUFFALO SOCIETY OF NATURAL SCIENCES Seah 


27, 449 A.D. Structure 10 is a rambling building added to at 
different times. An earlier part has Lintels 29, 30 and 31 while a 
later wing has Lintels 32 and 33. ‘The lintels of the first set are 
entirely glyphic and those of the second set have sculptured tableaux 
with human figures. The calculations on Lintels 29, 30 and 31 are 
obviously inter-related and they lead up to the important round 
number 9-17- 0- O- 0, 13 Ahau 18 Cumhu, March 27, 511 A.D. 
where there was a Venus coincidence. 


The Initial Series date with the Venus sign in the introducing 
glyph does not itself reach a significant phase of the planet but it 
may involve a comparison of two dates which do, namely: 


7- 3-15-17- 0, Sec taaYax; June=24>. 338-38. C. 

2-10- 1-13- 0 

9-13-17-12-10, 8 Oc Bere Oe 27, 449A, D- 
aa | 


9-13-18- 6-11, 4 Chuen 9 Zotz, June 24, 450 A.D. 


Here the first date is at the inauguration of the Venus calendar, 
on 13 Yax, practically coinciding with the summer solstice. This 
position is reached, as we see, by counting backward 19 calendar 
rounds from the recorded one of the initial series. The third date 
is that of another heliacal rising at exactly the same time in the 
‘natural year. While the two Venus dates are recovered on theo- 
retical grounds the association with the summer solstice is ramified 
by another circumstance. For on Lintel 30 there is a distance number 
which reached a date repeated several times at Yaxchilan and always 
in association with a hieroglyph that means the summer solstice. 
This date is 9-16- 1- 0- 0, 11 Ahau 3 Tzec, July 3, 492 A.D. The 
same date reaches the summer solstice exactly one calendar round 
later. On Stelae 11 and 12 there are other calculations with dates 
that interlock with the dates on the lintels we have just considered. 


The Venus Temples of Copan. A series of structures at Copan 
have to do with the coincidence of Venus with the round number 
9-17- O- O- 0, 13 Ahau 18 Cumhu, March 27, 511 A.D. One of 
these is Temple 22a which Morley named the Temple of Venus 
because of three large Venus symbols on the inner step which carries 
the inscription. The principal and only clear date is the one given 
above and with it is a hieroglyph of a new fire ceremony. There 
are, however, statements of 6 Ahau and 2 Ahau which may possibly 
refer to the nearby katun ending days of 9-14-0-0-0, 6 Ahau 13 
Muan, February 4, 452 when there was another Venus coincidence, 
and 9-16- 0- 0- 0, 2 Ahau 13 Tzec, July 9, 491. 


Temple 11 has several associations with the Venus cult. The 
date on the sculptured inner step, now in the British Museum, is 
that of the astronomical congress, namely 9-16-12- 5-17, 6 Caban 


26 VENUS AND THE MOON 


10 Mol, September 2, 503 A. D.t. On the doorway of the temple 
this date is repeated along with 9-14-15- 0- 0, 11 Ahau 18 Zac, 
November 17, 466, a position which seems to have received con- 
siderable attention because 18 Zac is the month position of the 
Historical era in the Maya year, and November 17 is the original 
location of 18 Kayab of the Venus calendar. The date on Stela N 
alligned with one stairway of this temple is 9-16-10- 0- 0, 1 Ahau 
3 Zip, May 18, 501. This has some slight connection with Venus 
since 3 Zip is an approximation of 6 Zip of the Venus calendarial 
position. Stela N also declared a katun ending in the past which 
coincides with the winter solstice (8-17- 0- 0- 0, 1 Ahau 8 Chen, 
December 22, 116 A.D.) and its collar has a statement of the posi- 
tion in the tropical year of the Historical era, namely 9-16-13- 4-15, 
6 Men 3 Yaxkin, August 6, 504 A. D., which should be considered 
with the anniversary of this era in the Maya year recorded on the 
doorway. 


Temple 22 at Copan was a gorgeous edifice with high relief 
sculptures partly restored by Maudslay from remains still in place 
about the inner doorway. On either side of the doorway a stooping 
atlantean figure sustains one end of a grotesque two-headed Venus 
monster. The symbols of the planet are prominently displayed on 
the legs of this monster. The body consists of five horizontal $’s 
each with a grotesque mannikin entangled in the folds and a smaller 
vertical S at each side. The outer doorway carried a similar decora- 
tion to judge from atlantean sculptures in the Peabody Museum of 
Harvard University, which are replicas of those still in place. Also 
the platform before the temple represents the lower jaw with teeth 
indicated on the upper parts of the stairway. In addition there 
were mask panels on the corners of the temple and probably the 
upper zone was a frieze of heavily sculptured gods and human beings. 
The high step of the inner chamber has four glyphic panels, ten 
glyphs to a panel, between death's heads. / 


Morley says that this building must be placed between the 
dedication of Temple 11 and Temple 22a. But both of these are in 
simpler style than Temple 22 and both seem, moreover, to have the 
same principal date, namely 9-17- 0- 0- 0, 13 Ahau 18 Cumbhu, 
March 27, 511 A.D. I suggest therefore that Temple 22 was 
erected to obviate the calamities due to the coincidence of Venus at 
the important round date 10-0-0-0-0, 7 Ahau 18 Zip, May 17, 570. 


*This most important date has pretty definite relations to Venus. Not only is 
September 2 an original position of the Venus heliacal rising at the time the calendar 
was inaugurated, but in the year 503 A. D. the Maya new year day 0 Pop fell on 
April 5, thus: 


9-16-12- meee 6 Caban 10 Mol, Sept. 2, 503 A. D. 


-1 
9-16-11-16- 7, 12 Manik 0 Pop, Apr. 5, 503 A? Dy 


An inferior conjunction of Venus with the Sun occtirred on Julian Day 1,904,863.9 
so that this new year began only three days after heliacal rising, perhaps regarded as 
a favorable condition. 


eee. 


BUFFALO SOCIETY OF NATURAL SCIENCES Ar 


The only recognizable time indication on the interior step of Temple 
22 is the day 5 Lamat, which recurs every 260 days. However, if 
the date of the temple is taken to be Katun 17 rather than Baktun 10, 
then we might have 


Mi 07 0-0, 13 Ahau 18 Cumhu, Mar: 27, 511 A.D. 
7- 8 

P40. 7- 8 5 -Lamat «1 Mol, AUeesL4e FLL ACD: 
Now this date 5 Lamat 1 Mol occurs three times on different 
monuments at Palenque. It is first placed three calendar rounds 
before the position given above and is then carried forward a great 
distance into the future and placed 8 days in advance of Pictun 1, 
thus:? 


1-0-0-0-0-8, > Lamat 1. Mol; Dee 257 45 12-A. DD: 
8 
1-0-0-0-0-0, 10 Ahau 13 Yaxkin, Dee, 1%, 4512 A.D: 


Here it is associated with a new fire ceremony as will be shown 
later. I think it not impossible that this complex is intended in 
the cryptic day sign on the step of Temple 22. 


Venus Monster Altars at Copan. The three altars called G*, G? 
and G* are representations of plumed Venus monsters, carved on the 
two sides and across the edges of laminar blocks of stone. Altar G', 
the largest and most elaborate of the lot, has at one end a conven- 
tional reptile head which probably symbolizes a dead Sun, and at 
the other a smaller one which symbolizes a living Venus. The draw- 
ing is practically the same on the two sides of the block, and as has 
been said, the details carry across the edges which are treated stencil 
fashion. Between the terminal figures is a double column of glyphs. 
The larger reptile motive is an immense head with elongated and 
fantastic upper jaw and a short lower jaw resting upon a leg of bare 
bone. The lower jaw and the end of the nose also indicate death 
according to the Maya conventions. Seated in the open mouth of 
this monster is a small figure of the Sun God. The smaller, or rear 
head, is of the same general type but there is no death symbolism 
and the eyes on either side contain the Venus sign. In the open 
mouth is a battered head possibly intended for the Sun God. 


Altar G* pictures a two-headed plumed serpent of symmetrical 
design, with the body arched and with a block of four glyphs under 
the arch. Altar G* follows the same pattern as G? but is somewhat 
smaller in size. On neither of these monuments is there any actual 
symbol of Venus or the Sun comparable to the ones on Altar G', 
but the subject is a mere variation on the theme of the Venus 
Monster and the dates have rather obvious significance in that they 
occur on other monuments where planetary symbolism is emphatically 
presented. 


1The date 10 Ahau 13 Yaxkin is recorded in the Dresden Codex on pages 60 
and 70 where the same Pictun 1 may be intended. 


28 VENUS AND THE MOON 
The time positions recorded on these three monuments are all 
of the period-ending type, as follows: 


Altar’ G*- -9-16-15-907-0.- - 7 "Ahaus18 Pop; Apt. 22, )3065 

9-17- 0- O- 0, 13 Ahau 18 Cumhu, Mar... 27,9 ieee 
Altar G? 9-18- 5- 0- 0, 4 Ahau 13 Ceh, Nov. 16, 335 ALD: 
Altar G’ 9-18-10- 0- 0, 10 Ahau 8 Zac, Oct: '20;= 540" fae 


The associations with Venus involved in the dates of Altars G* 
and G? are more obvious at first sight than that of Altar G*. The 
portentious katun which ended while Venus was passing from eve- 
ning to morning star is recorded on Altar G* and it will be remem- 
bered that we have already found this date emphasized in connection 
with the planet on several other monuments at Copan as well as at 
Yaxchilan.1 Whether the third hotun of Katun 16, also recorded 
on G*, had significance in the Venus cult is doubtful. 


Altar G? deserves to be bracketed with the famous Great Turtle 
Altar, so-called, of Quirigua. Both are Venus monsters and both 
bear the. same date which recovers 4 Ahau of the Mundane era, 
13 Ceh of the era of the Chronicles and reaches November 16, a 
close approximation to the original position of 18 Kayab at the 
inauguration of the Venus calendar. The date is also found on 
Altar 2 of Cancuen and on the newly discovered Stela 12 of 
Piedras Negras. It is also the probable date of the three altars from 
Lubaantun, now in the Peabody Museum at Harvard. The sculpture 
following that of the altar at Cancuen pictures the building of a 
ceremonial fire. 


The date on Altar G' marks the half-way stage between the 
culminations at 9-17- 0- 0- 0, 13 Ahau 18 Cumhu, March 27, 511 
and 10- 0- 0- 0- 0, 7 Ahau 18 Zip, May 17, 570. The text on 
this altar contains more than one detail pointing to Venus. One 
glyph is a somewhat decorative full-form symbol of Venus com- ~ 
parable to a glyph on Altar R. 


Altar W? at Copan is another variation on the Venus monster 
motive. On the face of this monolith is seen a crocodile-like front 
head and the rear head in the likeness of the Long-nosed God with 
a long jaw, while in the center of the design is a front view repre- 
sentation of the Sun God with the solar symbol on his forehead. 
The back and both ends of the monument carry hieroglyphs but the 
only decipherable part is the front end where a distance number 
9- 4 leads from a calendar round date 6 Ahau 13 Kayab to a day 
6 Kan. This addition can be put in the following chronological 
setting in which the calendar round date strikes the end of a hotun: 


9-07 5.-, 0-90; 6. Aha 13 Kayan: Feb. 28, 316 Ac: 
9. 4 
9.17% Se OF 4. 8 Kan » 12 Mol, Aug. 31, 7 326A 


1The date 9-17- 0- 0- 0, 13 Ahau 18 Cumhu, March 27, 511 is recorded at Copan 
on Temple 21a, the Reviewing Stand on the Pyramid of Temple 11, Altar Z and 
Altar G*; at Yaxchilan on Lintel 31; at Piedras Negras on Stela 13; at Quirigua on 
Stela E, at Seibal on Stela 6 and at Nakun and Honradez on Stelae 7 and 
respectively. In nearly every case the reference to Venus is clear. 


BUFFALO SOCIETY OF NATURAL SCIENCES . 29 


The hotun date has some interest in connection with the Venus 
calendar by reason of the 13 Kayab and at this time Venus was 
shining her brightest as morning star. The second date suggests a 
correlation with the second or third setting of the astronomical base 
line but is not true to the exact day. 


Several altars associated with stelae at Copan are of the Venus 
Monster type, the most conspicuous being the altar of Stela M. 
There are a few glyphic cartouches on the altar but none are de- 
cipherable. The only clear date on Stela M is a hotun ending without 
any marked reference to Venus. I believe, however, that there are 
additions of 2 tuns and then of 8 days leading to two dates which 
exactly state the heliacal setting of Venus as evening star and the 
heliacal rising as morning star. The whole record appears to be: 


9-16- 5- 0- 0, 8 Ahau 8 Zotz, June 12, 496 A.D. 
2° D4 0 

ie /-)0- 0, 13 Ahau 18 Zip, Tunes 2,.- 498° AD: 
8 

O16-)7- 0-8, 8 Lamat. 6 Zotz, June 10, 498 A.D. 


OTHER USES OF THE VENUS MONSTER MOTIVE 


The Venus Monster motive is rather widely distributed on 
monuments of the First Empire. As a celestial canopy it is promi- 


nent at Yaxchilan, Piedras Negras and Palenque, while at Copan 


and Quirigua the most striking uses are in altars. I give a list of 
the principal occurrences with dates and brief comment. 


Yaxchilan. Stela 1: Sun, Moon and Sky God above the 
canopy. Ceremonial bar of the dead serpent type. Flood symbol 


‘in hand of human figure. Venus title in introducing glyph. Dates: 


Initial Series. 9-16-10- 0-0, 1 Ahau 3 Zip, May 18, 501 A.D. 
A record of 6 Ahau may mean: 


9-14- 0- 0- 0, 6 Ahau 13 Muan, Feb. 4, 452 A. D. 


Stela 4: Sun, Moon and Sky God above canopy. Venus 
symbols attached to lower side. Flood symbol in hand of human 
figure. Ceremonial bar of dead serpent type. Date missing, possibly 
Katun 14 or Katun 17. 


Stela 6: Sun, Moon and Sky God above canopy. Flood 
symbol in hand of human figure. Date, uncertain. 


Stela 11: Sun, Moon and Sky God above canopy. Large 
Venus sign below canopy. Title of introducing glyph is summer 
solstice. Dates have marked Venus significance, 9-16- 1- 0- 0, 
11 Ahau 8 Tzec, July 3, 492 A.D. becomes June 22, one calendar 
round ahead. An original month position of Venus calendar is 
found in 9-15-19 1- 1, 1 Imix 19 Xul, August 4, 490 A. D. 


30 VENUS AND THE MOON 


i Piciess Negras. Stela 6: Serpent bird above canopy, he dee : 
of monster fall down over throne, flood symbol in the mou 


Stela 11: Serpent bird above canopy, heads of monster fa 
down over throne, flood symbol in the mouths. Date 9-15- O0- 0- 0, 
4 Ahau 13 Yax, October 22, 471. Approximation to 12 Yax of 
Venus calendar. 


Stela 14: Serpent bird above canopy, heads of monster fa oe 
down over throne, flood symbol in the ues Sun She ae 
sized at either side. 

18 Mac, December 12, 530 A. D. 


Stela 25: Serpent bird above canopy, heads of monster a 
down over throne. Two dates certain but apparently others. — No 
Venus significance disclosed. 


Stela 33. Throne apparently of celestial canopy ie but 3 in ; 
profile. Two dates but no Venus significance disclosed. 


Palenque. Stucco ornament in Palace over doorway, Pe 
symbols on legs of monster, but no accompanying date. ee Ven 
Monster as headdress in Temple of Inscriptions. oe 


Seibal. Stelae 9 and 10 have ceremonial bars hich may se 
intended to represent the Venus Monster. The date in both cases 
is 10- 1- 0- 0- 0, 5 Ahau 3 Kayab, January 31, 590 A.D. whic yo 
may be considered an approximation of January 28 in the orgie a 
Venus calendar. oo a 

Naranjo. Stela 8 has a variation of the Venus cae as 
headdress of the human figure with Venus glyph over a face dec 
rated like the God of the Number 7. The principal date 
9-18-10- 0- 0, 10 Ahau 8 Zac, October 20, 540. This is the da 
of Altar G' at Copan that is a Venus monster. Also 11 Ah: 
13 Yax is recorded. This is a Venus month posi 73 tuns fro 
Katun 15 as follows: . 


9-15- @ 0 0, 4 Ahan Ds Yax, Ope 225 471 A D. 
3-13- O- O 
9-18-13-. 02 0,- Li-Ahau- 83 Yar. Oct: Ton gas iP oe 


The calculations of this monument interlock with those of ‘St 
Gvand 7, 


Stela 32. The throne is here concerned largely Bt o Venus 
monster motive and some of the dates are pretty clearly i 


Tikal. Lintel 1 of Temple Il. Venus Monster ae 
throne. The leading date is 9-15-10- 0- 0, 3 Ahau 3 Mol, A 
30, 481 A.D. and the principal concern seems to be with ‘the a 


* i> 


BUFFALO SOCIETY OF NATURAL SCIENCES 31 
line. O Pop on April 8 is lifted one day to reach April 9. But 
August 30 is the reciprocal date of April 12 and this is the emphatic 
position of the Venus calendar in the tropical year. 


Quirigua. Stela H. Small celestial canopy on the back over 
seated figure: no Venus signs, however. The date is 9-16- 0- 0- 0, 
PeAnan 13 Tzec, July 9, 491 A. D. 


Altar O. An altar in the form of the Venus Monster with the 
date 9-18- 0- 0- 0, 11 Ahau 18 Mac, December 12, 530 A. D. 
I do not know how the Venus significance is found but see Stela 14 
at Piedras Negras. 


Altar P. Elaborate Venus Monster, details of smoke scrolls in 
over-lying designs, ceremonial fire as title in Initial Series introducing 
glyph and elsewhere in text. Principal date 9-18- 5- 0- 0, 4 Ahau 
13 Ceh, November 16, 535 A.D. This gives the Maya anniversary . 
of the era of the Chronicles, 9- 0- 0- 0- 0, 8 Ahau 13 Ceh, Feb- 
ruary 10, 176 A.D. and November 16 is about at the original 
position of 18 Kayab of the Venus calendar. The elaborate glyphs 
of the sides of the monster symbolize Baktun 10 with the Venus 
coincident and a dead hand holds out four days, thus: 


poeHe007 0-0... 7 Ahau 18. Zip; Mayet 7s 2370: AD: 
4 
10- 0- 0- O- 4, +11 Kan 2 Zotz, Mavala 51 Os Fe 125 


This is not sufficient, however, to reach the heliacal rising. The 
Mundane era and the era of the Chronicles are declared (C9b and E9) 
and several other dates. 


Copan: see discussion above for the principal examples of the 
Venus monster motive. 


ROUND NUMBER APPROXIMATIONS 


Round number dates are pretty clearly involved in the Venus 
cult when they give approximations to 18 Kayab, 12 Yax, 6 Zip, 
5 Kankin and 19 Xul and to November 16, June 23, January 28, 
September 3 and April 12 which were astronomical positions of 
Venus at the time of the inauguration of the Venus calendar. For 
the First Empire the dates that receive such emphasis are the 
following. 


RouND NUMBER APPROXIMATIONS TO ORIGINAL VENUS POSITIONS 
IN THE Maya YEAR 


8-16- 0- 0- 0, 3Ahau 8Kankin, Apr. 5, 97 A.D.. 3over 4 Kankia 
BiG 15> 0+ 0, 8 Ahau 13 Yax, Jan. 18,112 A.D., lover 12 Yax 
8-17-10- O- 0, 13 Ahau 18 Xul, Oct. 31,126 A.D., 1 under 19 Xul 
feeers- 0+ Of -5 Ahau / 3. Zip, Aug. 13,141 A.D., 3 under 6 Zip 
8-19- 0- O- 0, 10 Ahau 13 Kayab, May 26, 156 A.D., 5 under 18 Kayab 
9- 4- 0- 0O- 0, 13 Ahau 18 Yax, Dec. 18, 254 A.D., S over 13 Yax 
9- 4-15- 0- O 9A.D., 4o0ver 19 Xul 


wire arn s a. axkin, Oct ats 26 


co 
bo 


— pet — — — 


— pe 
OV SORSAOASAOS ROWS 


ntsieea Cakes pk peek hea pak 
WNK OIA AAWWNN COT TIA~ 
‘ ‘ ‘\ ‘\ ‘\ ‘ ‘ ‘ . ‘ ‘\ %, A + ‘ ‘ 7 


SSSYOVYYVoVoOoVooOoO© 
—" 


a a 


ROUND 


co 
‘ 
oa | 


Se OdO~IRMA ANY OITIYVANH COD 
‘ x s ‘ ‘ ‘ \ x ‘ ‘ ‘ x x x ‘ . gree al ‘ 
— 


—— 
MOoouNodoowuwdonuwouvrorwrvwvonwed 
‘\ ‘ s ‘ ‘X ‘\ 7 ‘\ ‘\ + ‘\ ‘ ‘ ‘ + ‘ ‘\ + ‘ 


— — pe 


SSOOOGVGVOOVVoOoewooooyey 
y ee ee 


— 
_— 


~ 


SSSOSSOSSSSSSSSSOOS 


iy “ v . ’ v w 


. 


. v y . . 


. 


SCOO90S SSCS SSeoeeoessZsfs 


10 Ahau 
2 Ahau 
7 Ahau 

12 Ahau 
4 Ahau 

10 Ahau 
2 Ahau 
7 Ahau 

12 Ahau 
4 Ahau 
9 Ahau 
1 Ahau 
6 Ahau 

11 Ahau 
4 Ahau 
9 Ahau 
1 Ahau 


VENUS AND 


8 Zip, 

18 Kayab, 
3 Kankin, 
5 1 ax, 

13 Xul, 

8 Yaxkin, 

13 Zip, 

3 Cumhu, 
8 Kankin, 


13 Kankin, 
18.7 ax: 
3 Yaxkin, 


THE MOON 

July 14,284 A.D., 2over 6 Zip 
Apr. 27, 299 A.D., exact 

Feb. 8,314A.D., 2 under 5 Kankir 
Nov. 21, 328 A.D., 4 under 12 Yax 
Sept. 4,343 A.D., 6 under 19 Xul 
Sept. 1,412 A.D.,10 over 19 Xul 
June 15,427 A.D., Tover 6 Zip 
Mar. 28, 442 A.D., 5 over 18 Kayab 
Jan. 8,457 A.D., 30ver 5 Kankin 
Oct..22, 471 A.D, 1 over seria 
Aug. 4,486 A.D., 1 under 19 Xul 
May 18,501 A.D., 3 under 6 Zip 
Feb. 28, 516 A.D., 5 under 18 Kayab 
Dec. 12, 530 A.D., 7 under 5 Kankin 
Dec. 10,599 A.D., 8 over 5 Kankin 
Sept. 23,614A.D., 6over 12 Yax 
July 6,629 A.D., 4over 19 Xul 


NUMBER APPROXIMATIONS TO ORIGINAL VENUS POSITIONS 


SSSSSSSSSS SSS SS SSS SS 


we v 


v 


essssssss 


wa 


~d wv . 


v 


Seo S oOo Oop oss 


3 Ahau 
12 Ahau 
4 Ahau 
5 Ahau 
10 Ahau 
6 Ahau 
11 Ahau 
3 Ahau 
12 Ahau 
4 Ahau 
5 Ahau 
10 Ahau 
6 Ahau 
11 Ahau 
3 Ahau 
12 Ahau 
4 Ahau 
9 Ahau 
5 Ahau 
10 Ahau 


8 Kankin, 
8 Zotz, 
18 Cumhu, 


IN THE TROPICAL YEAR 


Apr. 5, 97 A.D., 7 under Apr. 12 
Sept. 8,136 A.D., 5 over Sept. 3 
June 22,151 A.D., 1 under June 23 
Sept. 7,205 A.D., 4 over Sept. 3 
June 20,220 A.D., 3 under June 23 
Nov. 23, 259 A.D., 7 over Nov. 16 
Sept. 5,274 A.D., 2 over epee 
June 18, 289 A.D., 3 under June 23 
Nov. 21, 328 A.D., 5 over Nov. 16 
Sept. 4: 343 A.D., lover Sept. 3 
Nov. 19, 397 A.D., 3 over Nov. 16 
Sept. 1,412 A.D., 2 under Sept. 3 
Feb. 4,452 A.D., 7over Jan. 28 
Nov. 17, 466 A.D., lover Nov. 16 
Aug. 30, 481 A.D., 4 under Sept. 3 
Feb. 2,521 A.D. 5 over eee 
Nov. 16, 535 A.D., exact 

Aug. 29,550 A.D., 5 under Sept. 3 
Jan. 31,590 A.D., 3 over Jan. 28 
Nov. 14, 604 A.D., 2 under Nov. 16 


KATUN APPROXIMATIONS TO ACTUAL INFERIOR Con JUNCTIONS 
OF VENUS 


— 


PSOCOOOGOV OSE 
ce eek oe ee ‘ 
OTE TOMI OD 
Peoeeoooee 


tat et 


*This would be near the brightest phase of Venus as morning star. 
this phase was ceremonially observed appears doubtful. 


POSSSSOSSOS 


2S 


1 


y 


. 


1 


v 


~) 


1 


J 


a 


. 


coo9c9o9o°o09 


3 Ahau 8 Kankin, 
0 Ahau 13 Kayab, 
4 Ahau 13 Uo, 


1 Ahau 18 Tzec, Sept. 
5 Ahau 3 Chen, Oct. 
2 Ahau 8 Ceh, Dec. 
6 Ahau 13 Muan, Feb. 
3 Ahau 18 Cumhu, Mar. 


7 Ahau 18 Zip, 
1 Ahau 3 Yaxkin, 


Apr. 


5, 97 A.D., 35 days after Inf. Conj.’ 
May 26, 156 A.D., 31 days after Inf. Conj. 
July 17, 215 A.D., 29 days after Inf. Conj. 

5,274 A.D., 24 days after Inf. Conj. 
28, 333 A.D., 18 days after Inf. Conj. 


15, 392 A.D., 11 days after Inf. Conj. 
5 days after Inf. Conj. 


4,452 A.D., 
Zi, iA ee 


At Inferior Conj. 


May 17,570 A.D., 2 days before Inf. Conj. 


tale 6,629 A. ie 


5 days before Inf. Conj. 


namely that of Stela 9 gives a position 20 days after heliacal rising. 


Whether 
One early record at Uaxactun 


BUFFALO SOCIETY OF NATURAL SCIENCES 33 


It will be observed that 8-16- 0- 0- 0, 3 Ahau 8 Kankin, 
April 5, 97 A.D. is found in all three lists. It also corresponds 
to the vernal station of the first arrangement of the astronomical 
base line at Copan and appears to be reached by a special line of 
observation at Uaxactun where two monuments record the date, 
namely Stelae 18 and 19. Stela 5 at this early site records April 12, 
the highly emphasized date of the Venus calendar in the following 
relation: 


7.0, Renae oR ath. tat AT eae 8) AN, 
-12 
125 BLED 15 Kankin, Piresls. kon os. 


The next katun ending emphasized in two of the lists is 
8-19- 0- 0- 0, 10 Ahau 13 Kayab, May 26, 157 A.D., recorded 
on Stela 17 at Uaxactun and reached by subtraction on the Hiero- 
glyphic Stairway at Seibal in what is possibly a calculation of Venus 
import. The Initial Series of Stela 3 at Tikal may have an implied 
connection since it registers a date 73 tuns later, thereby reaching 
the same month position and very nearly the same relation to the 
planet. Katun 2 of Baktun 9 is found on Stela 9 of Tikal but | 
am not able to discern any Venus hieroglyphs in the inscription. 
Venus appeared as morning star on the summer solstice about 25 
days before this date. 9- 4- 0- 0- 0, 13 Ahau 18 Yax, December 
18, 254 is the point of departure for the long series of the Temple 
of the Inscriptions at Palenque, which touches many of the subse- 
quent dates in these lists. 


Most of the round numbers of interest in the Venus cult which 
are shown in the preceding lists are accompanied by Venus glyphs 
except in a few cases where a greater interest intervenes. Where 
the numbers are declared by the Initial Series, or are prominent in 
inscriptions which begin with Initial Series, the designation is often 


VL aE 


Fic. 5. TITLE GLYPHS OF THE SUMMER SOLSTICE. 
Left to right: Stela 1, Los Higos; Lintel 1, El Cayo; Stela 11, Yaxchilan. 


accomplished by means of the title, a name here applied to the 
variable element occupying the central position in the introducing 
glyph above the tun sign and between the comb-like elements. 


TITLE GLYPHS 


The validity of the title glyph, as a true index of subject 
matter, may be open to some doubt and I therefore think it proper 
to give a few cases besides those which involve glyphs in the Venus 


34 VENUS AND THE MOON 


— a 


series. _I first direct attention to three inscriptions which have th 


chine like a tun, but recognizably different. The first inscriptio 
at Los Higos has two dates, the first exactly equalling the summe 
solstice, namely: | ee. 
9-17-10- 7-0, +9 Ahau-. 3. Tzec; June:.22, aoe ALT. 

7- 0 subtract 

9-17-10- 0O- 0, 12 Ahau 8 Pax, Feb. . 2, 320 vies 

The second inscription is Lintel 1 at El Cayo, the first three dates 
ot which are 


9-16: O- 2-16, 6 Cib | 9 Mol, Sept: 3, 491 Acme ae 


11-P710 | ae 
9-16-12- 2- 6, 13 Cimi 19 Zotz, June 23, 503 A.D. 
304 


9-16:12- 4-10, 5 Oc 3 Yaxkin, Aug. 6, 503 A, Dias ne ht 


April 9 or to a position in the Venus calendar. The third ee 

is found on Stela 11 at Yaxchilan where the Initial Series date 

registers 9-16- 1- 0- 0, 11 Ahau 8 Tzec, July 3, 492. This seems — 
far off from the summer solstice but by adding one Salendas cee 
the proper location is found, namely: a2 

9-16- 1-0-0, 11 Ahau 8 Tzec, ‘July 3, 492 Ae a 

Reldehae 0 | rere 

9-18-13-13- 0, 11 Ahau 8 Tzec, June: 22, 744 ia Rios 

Now this date in calendar round form is found several times a 
Yaxchilan. On Stela 12 it occurs in combination with another date, — 

the two giving about the same arrangement as the second and thir ae 

dates on the El Cayo lintel, namely: ley 3 
9-18- 3-12-14, 6 Ix 12 Yaxkin, Aug. 17, 534 A.D. ey 

10- O- 6 | 

9-18-13-13- 0, 11 Ahau 8 Tzec, June 22, 544 A. De 


added to it also reaches the summer solstice, thus: 


9-15-10-17-14, 61x 12 Yaxkin, Aug. 19, 482 A. D. 
6%, Oo 
9-15-17-16-14, 10 Ix 17 Zotz, June 23, 489 A. D. 


ways with the summer solstice the hieroglyph that Pe ie title 
element in the three inscriptions is prominent. It is also promin 
at Quirigua in connection eon ah frequently repeated Fie: apes 


namely: 


BUFFALO SOCIETY OF NATURAL SCIENCES 3D 


915- 6-14- 6, 6, Cimi 1° 4-Tzec, July 3, 478 A.D. 
I find a perhaps more impressive example of its use on the Temple 
of the Cross at Palenque. After dealing with a date near the epoch 
of the Mundane era, which demonstrates the ability of the Maya 
astronomers to state definite times of the tropical year so far in the 
past, the record gives: 


iene 5-03-25 5 9 Tk 15 Ceh, Dee 2 be 261973. G: 


which is the winter solstice. But this statement is associated with 
a summer solstice glyph capped by an S-shaped detail which seems 
elsewhere to mean reversal. And it happens that 15 Ceh coincided 
with the summer solstice at the epoch of the Mundane era and the 
distance number gives a time sufficient for 15 Ceh to move half way 
around the tropical year in terms of the Maya uncorrected year. 


The titles in introducing glyphs are of several kinds but after 
all the range is not wide and Venus glyphs are perhaps more com- 
mon than any other forms, especially the type of Venus glyph which 
pictures the grotesque head of the Venus monster. There are Sun 
glyphs and Moon glyphs and others that represent interlacing. One 


Fic. 6. TITLE GLYPHS OF THE CEREMONIAL FIRE. 


At left title of the Tablet of the Sun at Palenque; title of Lintel 2 at Piedras 
Negras. Center, passage in the Temple of Inscriptions at Palenque. At right, 
title of Altar P at Quirigua and glyph of Baktun 9, Temple of the Sun at Palenque. 


kind deals with a jaguar head or body. Another shows the face of 
the God of the Number 7 who rules over the Historical era. Still 
another title is the ceremonial fire. 


I close the brief comment on the title glyphs with a few relating 
to ceremonial fires. Three examples are notable. The introducing 
glyph on the Tablet of the Sun at Palenque shows a ceremonial fire 
as headdress of a grotesque face. The Initial Series reaches a date 
just four days in advance of the winter solstice, namely: 


36 VENUS AND THE MOON 


1-18- $-"3286, 13: Gimi*19" Geh; Dec. 25, 2619 B.C. 


On Lintel 2 at Piedras Negras the title of the introducing glyph is 
clearly meant to portray the bundle of sticks with the smoke curls 
of newly kindled fire issuing from the top. The Initial Series date 
reaches the same position in the Maya year and in the tropical year 
as the one at Palenque but does not arrive at the same day, namely: 


Q-11- 6 2- 1, 3 Imix 19 Ceh, Dec. 25, 398=Ac 


If two grand calendarial cycles of 29 calendar rounds each had been 
used the day 13 Cimi of the Palenque statement would have been 
returned. As it is the correspondence is 3 civil years over this limit 
but the results still fall with December 25 of the Gregorian calendar. 
A third correspondence is found, not in an Initial Series but in a 
rather complicated calculation of the Temple of Inscriptions at 
Palenque reaching forward into the future to the date 5 Lamat 1 Mol 
placed 8 days in advance of the round number 1-0-0-0-0-0, 10 Ahau 
13 Yaxkin, December 17, 4512 A. D., where it also reaches Decem- 
ber 25 and is combined with the new fire hieroglyph. 


But ceremonial fires were built at other times than December 
25. They seem to have been built at terminal or beginning dates 
(Imix-Ahau signs are frequently combined with smoke scrolls and 
Imix and Ahau are Alpha and Omega, First and Last). Especially 
such fires were built in connection with the terminal dates of baktuns. 
One set concerns 9- 0- 0- 0- 0, 8 Ahau 13 Ceh. The separate glyphs 
of the era of the Chronicles all have smoke curls at the top and the 
complete fire bundles are shown in connection with the chronological 
recordings of Baktun 9. Also the new fire ceremony is used with 
dates that recapitulate the 13 Ceh of this baktun. Especially prom- 
inent in this regard is the Initial Series of Altar P at Quirigua which 
has as title the fire bundle. It reaches, as we have already seen above, 
the date 9-18- 5- 0- 0, 4 Ahau 13 Ceh, November 16, 535 A. D. 
which also has significance in connection with Venus. Other fire 
bundles, not in introducing glyphs but in the running texts are some- 
times combined with ceremonial fires for the Venus cult such as 
9-14- 0- 0- 0, 6 Ahau 13 Muan, February 4, 452 A. D. and 
9-17- 0- 0- 0, 13 Ahau 18 Cumhu, March 27, 511 A. D., when 
there was an actual coincidence and even with 9-15- 0- 0- 0, 4 Ahau 
13 Yax, October 22, 471 A. D. when the connection with Venus was 
dilated through the month position 13 Yax. 


FURTHER EXAMPLES OF INSCRIPTIONS DEALING WITH VENUS 


An inscription which pretty clearly refers to Venus is that of 
the Leyden Plate, the title of the introducing glyph being a grotesque 
head with the combined Venus-Sun symbol for the ear plug. The 
date is: 


8-14- 3- 1-12, 1 Eb 0 Yaxkin, Nov, 27, = 60vAC 


BUFFALO SOCIETY OF NATURAL SCIENCES 37 


It will be observed that 0 Yaxkin is the day after the Venus month 
position 19 Xul and that November 17 is the original location of 18 
Kayab in the Venus calendar. 


Altar S at Copan is a nice example of an inscription referring 


Fic. 7. INSCRIPTION ON ALTAR §S AT COPAN. 

First two rows give the Initial Series 9-15-0-0-0, 4 Ahau 13 Yax, following an 
introducing glyph with Venus symbol. Third line, a, an unknown ending; 6b, Sum- 
mer Soltice over Caban (Earth); c, 5 katuns; d, Imix-Ahau with smoke scrolls; 
e and f, 7 Ahau 18 Zip. Fourth row, a, Baktun 10; b, unknown descriptive; c, 
Venus symbol with superfix; d, glyph with some such meaning as ‘‘heavenly round.”’ 


to Venus. The title is the head of the Venus Monster, and there 
are two dates declared as follows with the connecting number: 
aioe 02.07 0." 4 Ahau 13 Yax; O22. 47) ALD; 
5- O- O- O “ 
fo0-- 0-202 020 7 -Abau 18. Zip, May 17, 570 A.D. 


38 VENUS AND THE MOON 


The Imix-Ahau sign with smoke curls precedes the last date and the 
next to last glyph of the text is a winged Venus symbol of some- 
what decorative type. 


Altar M at Quirigua has no introducing glyph with title but 
the monument itself is a grotesque head of the Venus monster, the 
eye of which is modified into an Imix sign. This gives almost the 
same complex as Altar S of Copan. The first date is Katun 15 and 
there are 5 katuns which read an undeclared Baktun 10. Also there 
is a distance number. connecting a date which reaches November 15 
of the Venus calendar and 18 Zac of the Historical era, thus: 


9: 15- OOo * 4A had at ocoy ag. Oct: 22; 47a 
3- 2- O 
9-19". 3-. 2720; 6 Ahau 18 Zac, Nov. 15, 474 A.D. 
a *k * : 
9-15- 0- 0, 4 Ahan 13° Yas: Oct. 22) “4g ASD 
0O- 0 
10- 0- 0- 0, 7 Ahau 18° Zip, L390 Ae 


BiG. eS: NEW FIRE AND IMIX-AHAU GLYPHS AT KATUNS 
14 and 17. 


At left, passage on Stela 23 at Naranjo—Imix-Ahau and Ceremonial Fire in 
combination with 6 Ahau 13 Muan, end of. Katun 14. Center, Stela 1 at Yaxchilan 
—6 Ahau (13 Muan) -New fire. Right, inscription on Altar Z at Copan reading 
as follows: distance number 1-8-1; Imix-Ahau with smoke scrolls; 138 Ahau 18 
Cumhu; glyph with smoke element. Top, glyphs on Temple 22a and the Reviewing 
Stand at Copan, Imix-Ahau with smoke curls found in combination wth 9-17-0-0-0, 
13 Ahau 18 Cumhu. , 


Altar Z of Copan, already briefly referred to, belongs in the 
same category as the two just described. It is a rectangular plinth 
with a grotesque snouted face on the front side—undoubtedly 
intended for that of the Venus Monster. There is a conspicuous 


BUFFALO SOCIETY OF NATURAL SCIENCES | 39 


Imix symbol over the nose and in the headband the dotted smoke 
curls are prominent. The inscription consists of 12 glyphs covering 
the remaining three sides of the monument, the top and bottom 
being plain surfaces. The inscription begins with a distance number 
2 1- 8- 1 followed by the Imix-Ahau smoke symbol combined with a 

completion sign. After this comes the single date 9-17- 0- 0- 0, 
13 Ahau 18 Cumhu, March 27, 511 A. D., which fell in the dark 
period of the Venus revolution near inferior conjunction. The 
_ distance number is evidently intended to be counted both ways as 
follows: 


Por ior. 9-19, 12 Cauac 2 Zac, Ode) 2509) AD: 
1- 8 1 

9-17- 0- O- 0, 13 Ahau 18 Cumhu, Mare 27. 5 112 A-D: 
l- 8 1 

O-1J+ 1- 8- 1; 1 Imix 9 Mol, Aug, 29.55) 2 ACD: 


This bifurcated calculation restores the positions in the natural year 
of two round numbers, namely: 


9-15- 0- 0- 0, 4 Ahau 13 Yax, Oe 1? Ae ALD: 
iO. 0 
S310; 0-0, . 3Ahau. 3 Mol, Aug. 30, 481 A.D. 


_ +The second date August 30 pairs with the Venus date April 12 
along the line of sight at Copan. In glyph 8 of this inscription there 
is a Kin-Caan-Caban ideograph of the Sun at the horizon and in 
glyph 9 we see a Venus symbol combined with a Cauac or rain 
symbol meaning “relation of Venus to the natural year of the rains.” 


Venus signs of the normal type (i. e., those agreeing with the 
commonly recognized forms of the Dresden Codex) are found as title 
element in the introducing glyph on the following monuments: 


Lintel 29, Yaxchilan (See above for explanation). 
9-13-17-12-10, 8 Oc eel eee Oct. 27, 449 A.D. 
leer} subtract 


9-13-10- 0- 0, 7 Ahau 3 Cumhu, Mar. 28, 442 

Stela K, Quirigua 

9-18-15- O- 0, ge Anal ooo ty ax, Sept. 24, 549 
10-10 subtract ; 

9-18-14- 7-10, 1 Oc 18 Kayab, Feb. 26, 545 

Stela 1, Saccana 

ii e2-6 5-07, 02. - 9: Ahau 18. Yax, sept: 23;°613 A.D: 


9-13-16-10-13, 1 Ben 1 Chen, Sept. 25, 448 A.D. 
Altar K, Copan 
9-12-16 7- 8, S eLamatr on Las: NMoveu 34-428. A.D: 
Stela 24, Naranjo 
Orel 2eL0- "5-12, 4 Eb LO AY 3%, Oars 1422 -A. dD: 
P hea £t . 
Bel 205713707; 9 Manik O Kayab, Mar. 8, 428 A.D. 
1l- 8 1 
Wgee i 2 o76..cO: Lainat’s 1 Zotz, June 20, 439 A.D. 
2-14-12 
AL. 
A.D. 
“aya DP 


3 Not one of these five inscriptions registers an actual coincidence 
of Venus in a significent phase nor are the intervals between the 


40 VENUS AND THE MOON 


dates Venus intervals. But it will be noted that the Initial Series 
date in every instance falls in the month Yax. At the inauguration 
of the Venus calendar an heliacal rising took place on 12 or 13 Yax 
and we have found the recurrence of this position in the round num- 
ber 9-15- O- O- 0, 4 Ahau 13 Yax, symbolized by Venus glyphs. 
The first inscription given above has already been explained in com- 
bination with the dates on associated lintels in the same structure. 


The association on Stela K at Quirigua is a Yax date practically 
on the autumnal equinox associated with an 18 Kayab date, this 
latter having affiliations with the Venus calendar. I suspect that 
the two dates on this monument have a concealed significance as 
regard some other planet.t | The interval 10-10 has been explained 
as the number needed for intercalation of leap year days but this 
explanation is open to objections. 


At any rate the Venus glyph of Stela 1, Saccana forms an 
interesting commentary. This date is 3-10- 0- 0 in advance of that 
on Stela K and exactly reaches the autumnal equinox. Indeed, Blom 
found at Comitan a monument on which this date carries the 
equinoctial glyph. Now the interval of approximations in the Venus 
calendar is not 70 tuns but 60 tuns. The case is carried a step 
farther by the association on Lintel 29 at Yaxchilan when an 
interlocked date falls on September 25. In the example from Naranjo 
one association is with a date which nearly coincides with the sum- 
mer solstice. The day reached in two of our cases is Lamat, which 
has some special association with Venus. If some of these cases 
where the Venus hieroglyphs are quite clear seem unusually recon- 
dite it must be admitted that the lack of a true Venus interval 
between the dates presents an equal difficulty in any other system of 
correlation. . 


I reserve for later consideration several inscriptions in which 
the Venus calculations are interlocked with those of the moon. These 
will probably provide the type explanation that must be followed in 
several cases like the above. It appears that Maya astronomy was 
overlaid with astrological considerations and that the priests of 
those days sought the machinations of fate in the relative positions 
of planets. We will now proceed with the calendar of the Moon. 


THE LUNAR CALENDAR 


The apparent revolution of the Moon around the Earth, marked 
by the recurring phenomenon of the new moon, was used by the 
Mayas as the basis of a lunar calendar. This was. distinct from the 
civil calendar and may have been used for ceremonial purposes. The 
Mayas probably had a series of movable feasts which depended, like 
our Easter, on the phases of the Moon. 


19-18-15- 0- 0, 3 Ahau 3 Yax, September 24, 545 A.D. is a new moon date. 


- 
a, 
7 
ty 
v4 
ie 
3 


BUFFALO SOCIETY OF NATURAL SCIENCES 41 


Now the average duration of a lunar revolution is 29 days, 12 
hours, 44 minutes, 2.8 seconds. Twelve lunations fall nearly 11 
days short of a true year and primitive people whose principal 
interest is to keep the Moon in adjustment with the seasons have an 
occasional thirteenth month in their lunisolar calendars. In a second 
stage we sometimes find twelve conventional months of 30 days 
each. It has already been explained that an early month of the 
Mayas was reduced from 30 to 20 days but it must not be imagined 
that the Mayas lost their interest in the Moon from this convention. 
Indeed they rapidly developed ways of dealing with the Moon which 
command the highest respect of astronomers. 


Among other things they discovered independently the corres- 
pondence between 6940 days, 19 tropical years and 235 lunations 
with which the name of the Greek astronomer Meton is commonly 
associated. They were able to use this natural cycle with much 
greater facility than the Greeks by reason of a remarkable coinci- 
dence: in Maya notation 1 katun minus 1 tzolkin gives exactly 6940 
days. The subtraction can be written as follows: 


l- 0- 0- 0 = 7200 days 
Loa ese ot 2G eae 
19- 5-0 = 6940 


The interval of the Metonic Cycle is used prominently in several 
lunar calculations at Copan. 


A much more accurate and remarkable lunar cycle of the Mayas 
is developed on pages 51 to 58 of the Dresden Codex. Here a suc- 
cession of 405 lunations, amounting to nearly 33 years, is calculated 
in groups of five and six lunations, the former given as 148 days and 
the latter as 177 or 178 days. These are eclipse intervals and the 
purpose was evidently to form a table from which eclipses of either 
the Sun or Moon could be foretold. The count covers a total of 
11,960 days' and contains the tzolkin just 46 times. It therefore 
makes a reentering cycle as regards day names, and is capable of 
being used over and over again. By modern calculation 405 apparent 
lunar revolutions are only 0.112 of a day less than 11,960 days, 
therefore this Maya pattern. of the Moon’s motion will run for 
nearly 300 years before the accumulating error amounts to a day. 
Since the table is arranged to depart from three receding days, 
namely 12 Lamat, 11 Manik, and 10 Cimi, it has been assumed that 
the first of these could be used for 8 cycles, after which the calendar 
would slip down to the second day and be set for a second series 
of 8 cycles etc. The historical positions at which the elaborate 
calendar of the Dresden Codex was intended to apply have not 
been determined. The difficulty lies in finding an arrangement of 
solar eclipses that will fit:the eclipse indications. Professor Willson 
devoted much labor to this eclipse data but without effecting a 


1This is divided into approximate thirds (3986 and 3987 days) an interval after 
which eclipses return called by Willson the Maya Saroid. 


42 VENUS AND THE MOON 


chronological correlation capable of meeting all demands. It is 
highly probable, I think, that the Lunar calendar of the Dresden 
Codex will be found to have an adjustment to conditions at the 
beginning of the Thirteenth century in keeping with the adjustment 
with actual appearances of Venus found for Calendar B of the 
Venus table in the same manuscript. 


THE SUPPLEMENTARY SERIES 


Following the Initial Series declaration on many monuments 
of the First Empire is a Supplementary Series which clearly involves 
a lunar count. The last glyph, called Glyph A in Morley’s nomen- 
clature, is a moon having the numerical value 20 combined with a 
coefhcient 9 or 10 to make a 29 or 30 day month. Other glyphs, 
mostly lettered in reverse order, have numerical values as demon- 
strated by Teeple. These belong in short counts which do not 
exceed 6 or possibly 7 lunations,’ and which are assumed to fit into 
a pattern of eclipse probabilities similar to the one which finds 
expression in the Dresden Codex. Glyph C records complete luna- 
tions which may not exceed six. Glyph D states the number of 
days in an incomplete lunation which may not exceed 19. Glyph E 
without coefficient has the value of twenty days in an incomplete 
lunation and its coefhicients record the days above twenty. 


These lunations are not counted from a uniform series of bases 
nor do they reach true places of the moon in the correlation used 
ir. this paper. It has therefore been argued that the correlation was 
in error and an effort has been made to find another by the method 
of departing from a point where some one series coincided with a 
true phase of the Moon. Such a method, however, brings its own 
difficulties. In the first place it is not certain whether the days of 
the Moon are counted from new moon or full moon. In the second 
place the arbitrary selection brings no series of recorded eclipses into 
display. In the third place a correlation chosen to satisfy certain 
assumed conditions as regards the Moon fails to meet the historical 
evidence of double datings, both of the Sixteenth century and of 
ancient times. 


But there is the unconsidered possibility that the lunar calendar 
of the Mayas resembles their other calendars in being of the uncor- 
rected type so that the true positions of the Moon depart from the 
calendarial positions by the amounts of an accumulating error. In 
the present study the records of the Supplementary Series are 
explained as having an error of this type. 


Examining Supplementary Series found on monuments of the 
First Empire which record by Initial Series the same date, it is 
disclosed that they are frequently counted from different bases, i. e., 
the coefhcients of Glyph C, which give complete lunations, differ. 


1When Glyph C has the value six it is reduced by Teeple’s system to zero, 


hd 


BUFFALO SOCIETY OF NATURAL SCIENCES 43 


Total Days 
Glyph C Glyph D GlyphE of Base 
before Date 


_ Naranjo Stela 24 


1 18 rice ds 
So dare 0 19 (or 19+177=196) 
. a * * 
Piedras Negras Stela 1 3 0 8 117 
. is goat Ga 2 0 | 86 
x x x 
Quirigua Stela J 6 4 0 4 (or 4 + 178=182) 
Copan oa aM 5 5 0 153 
* * x 
Quirigua Stela E © 2 0 0 59 
eee 3 0 0 89 


Honradez 


ai will be observed that the maximum variation is one lunation, 
particularly if 6 C is counted as 0 C. 


~ Now let us examine the record of the last two monuments in 
still another light. In Oppolzer’s Canon of Solar Eclipses! a total 
eclipse with its line of centrality across Yucatan and Venezuela 
occurred in the year 511 A.D. on Julian Day 1,907,715 which 
reduces to the Maya date 9-16-19-14-11, 9 Chuen 9 Muan, Jan. 
17, 511 A.D. Since the initial series of Stela 7 at Honradez and 
Stela E at Quirigua record 9-17- 0- 0- 0, 13 Ahau 18 Cumhu, 
_ March 27, 511, the difference between the time of this eclipse (neces- 
sarily at the new moon) and the ending day of the recorded Katun 
is 69 days. In other words Maya number 9-17- 0- 0- 0 in the Long. 
Count really corresponds to 10 days after new moon or 4 days 
before full moon, whereas the statement of the Supplementary Series 
reaches the even lunation. 


The assumption has been made, I believe, that the lunations of 
the Supplementary Series were counted from the new moon, if so 
probably the observed new moon rather than the moment of the 
invisible conjunction of the Moon with the Sun. But the lunations 
may have been counted from full moon. If the difference between 
the calendarial moon and the true places—10 days over the new 
moon or 4 days less than the full moon—are to be explained by the 
accumulated error of an uncorrected lunar calendar then the least 
error would be found in connection with a calendar giving results 
slightly longer than a sum of true revolutions. Now the Lunar 
calendar of the Dresden Codex based on:the 11,960 day cycle, is 
the one concerning which we have the most explicit evidence and 
this is, in fact, enough longer than the true places to account for one 
_ day error in something like 300 years. Therefore it is possible that 


the lunar places were calculated in the Supplementary Series in 


accordance with this slightly erroneous Lunar calendar. If this 
_ theory is correct we should have complete parallelism with conditions 
in the civil and Venus calendar which are inviolate patterns. It 
is also possible that the Metonic cycle was used to form a kind of 


1T. R. von Oppolzer: Canon der Finsternisse Denkschriften der Kaiserl. Akad 
der Wissensch. Math-Naturw. Classe, Vol. CCV. Wien, 1887. 


44 VENUS AND THE MOON 


lunar calendar in which case the error would be much greater and 
the displacement also greater. 


Proof that numbers in the Supplementary Series were reached 
on the 11,960 basis, by means of a calendarial pattern rather than 
by concurrent observation, may be deduced from the fact that the 
three major Initial Series at Palenque recording dates thousands of 
years before the beginning of history are correct in Teeple’s tables. 
Here we must imagine that lunar statements were projected back- 
wards from an historical base corresponding to about 430 A. D. 
These three series are: 


Temple of Cross— 


12-19-13- 4- 0, 8 Ahau 18 Tzec, Feb. 7,°3379 BLG. 
Temple of Sun— 

1-18- 5- 4- 0, 1 Ahau- 13. Mac: Dec: 25, 2619 tes ce 
Temple of Foliated Cross— 

1-18-05: 3- 6, -13°Cimii19eGek, Jan.. 8) 261s 


INTERRELATIONS IN TABLES OF VENUS AND THE MOON 


The Lunar calendar of the Dresden Codex is a reentering series 
covering 405 lunations, 46 tzolkin, and 11,960 days, concerned 
primarily with intervals after which eclipses can recur. This table 
has in its preamble several dates in the Long Count which are found 
to be significant in Venus calculations. Conversely the preamble of 
the Venus calendar has dates of interest in calculations concerning 


the Moon. 


We have already seen that the original calendar of Venus 
departed from the month position 18 Kayab (and from four other 
positions at intervals of 584 days). In the codex the particular day 
1 Ahau 18 Kayab is designated for Calendar A. Calendar B is 
given a position in the preamble long before the true _ historical 
position where it actually coincides with the significant appearances 
of Venus. The date 1 Ahau 13 Mac can be placed exactly one 
cycle of the Lunar calendar away from the hypothetical position of 
1 Ahau 18 Kayab, namely: 


9- 9- 9-16- 0, 1 Ahau 18 Kayab, Apr: -12, 363-34, De 
1-13- 4- 0 11960 days 
9-11- 3- 2- 0, 1 Ahau 13 Mac, Jan. 29, 396, Ask: 


The first date is declared by distance number on page 24 of the 
Dresden Codex, this page being in the nature of an introduction to 
the Venus calendar. While 1 Ahau 13 Mac is not stated to fall in 
the arrangement given above, we do find the date in the Initial 
Series of the tablet of the Foliated Cross at Palenque, occupying the 
same position of the natural year but just 58 calendar rounds distant 
in the past. Since 58 calendar rounds are twice the Maya cycle of 
concordance (29 & 52 &K 365 ==1508 calendar years = 1507 tropi- 
cal years) the same Maya and Gregorian statements are brought 


BUFFALO SOCIETY OF NATURAL SCIENCES 45 


together. Also it is interesting to note that this restores positions 
of the Moon within .64 of a day. 


It may be pure accident that the first distance number in 
Column D of page 24, which amounts to 416 calendar years or 260 
Venus revolutions, gives recapitulation of January 9 when added 
to the stated position of 1 Ahau 18 Kayab, thus: 


9- 9- 9-16- 0, 1 Ahau 18 Kayab, Apr. 12, 363 A.D. 
Tdeci-id- 0 
10-10-11-12- 0, 1 Ahau 18 Kayab, eae we read AF pre Wed DE 


I believe this harping on January 8 or 9 (according to the inequalities 
of the Gregorian equivalents) reveals the important position used 
in calculations dealing with the Moon during the First Empire. 


There are two other positions of 1 Ahau 13 Mac which follow 
from the numbers in connection with the Venus table. The second 
distance number in Column E of page 24 is a proper interval, thus: 

9- 9- 9-16- 0, 1 Ahau 18 Kayab, Apr. 12, 363 A.D. 
9-11- 7- O 
9-19- 1- 5- O, 1 Ahau 13 Mac, Dec 245 51 AnD; 


Lastly Calendar B of the Venus table finds 1 Ahau 13 Mac at 
the summer solstice and likewise in touch with actual heliacal risings 
of Venus as morning star. 


We now proceed to the Lunar table, more especially to the 
introductory material in the upper half of pages 51 and 52. Here 
are six interlocking red and black numbers counted from the Mun- 
dane era, one pair being on the left and two pairs on the right. 
Between them is a section of 11 shorter numbers which are primarily 
multiples of 11,960 although three may be errors or intentional 
variations from exact multiples. Several emendations in the numerals 
of the six long numbers are necessary but these have long since been 
agreed upon by Forstemann, Bowditch and other students and need 
not be explained at this time. 


The first column reads down as follows: 4 Ahau, 8 Cumhu, 
12 Lamat, 8 days, knotted Imix. Then come the numbers 
8-16- 4- 8- 0 and 10-19- 6 1- 8 with 12 Lamat repeated at the 
bottom of the column. These numbers count from the Mundane 
Era, 13- 0- 0- 0- 0, 4 Ahau 8 Cumhu, October 14, 3373 B.C. 
In one case 4 Ahau 3 Zip is reached and when the 8 days are 
added we get 12 Lamat 11 Zip. In the other case 12 Lamat 6 Cumhu 
is reached and when the 8 days are subtracted 4 Ahau 18 Kayab is 
obtained. The transformation into Gregorian dates, with the age 
of the Moon? appended in the last column yields: 


1550420 days — 19638 lunations less .64 of a day. 

2T have used Oppolzer’s Canon of Eclipses to give new moon positions within 6 
lunations, reducing these to the meridian of Copan. Order in error of the Moon may 
interfere but the accuracy is sufficient for the present purpose. The age index gives 
the phase of the Moon at the beginning of the day in question. 


46 VENUS AND THE MOON 


- 0, 4 Ahau 8 Cumhu, Oct. 14, 3373 B. C. 
) 


B 8-16 > 4 Noe 3 Zip, Aug. 23, 101 ASD 
8 ad 
C 8-16- 4 S12): Lamats 117 Zip. Aug. 31, 101° A0DS ie 
ek oe 
A 13- 0--0- O- 0, +4 Ahau 8 Cumhu, Oct. 14, 339 yee 
10-19- 6 1- 8 add 
D 10-19- 6 1- 8, 12 Lamat 6 Cumhu,° Nov. 24, 950 A.D. 10.4 
subtract 
E 10-19- 6 1- 0, 4 Ahau 18 Kayab, Nov. 20, 950 A.D. 2.4 


Here the month position 3 Zip of Date B belongs in the Venus 
series of emphatic positions in the Maya year and 8 days is the 
interval of obscuration of Venus at inferior conjunction while the 
day Lamat, reached by the addition, is again closely connected with 
this planet. August 31, to be thought of as August 30 since the 
year 101 comes at a time of uneven correction in the Gregorian 
calendar, is a position in the natural year reached by the final 
adjustment of the astronomical base line at Copan. — Its reciprocal 
date of sunset reading along the adjusted base line is April 12, the 
prime position of Venus in the natural year which is treated in the 
Venus table of the Dresden Codex, as well as on several important 
monuments. Date D records Lamat, the sacred day of Venus, and 
Date E reaches an actual heliacal rising of this planet on its special 
month position 18 Kayab. It is this date which gives us the historical 
location of Calendar A of the Venus table already sufficiently 
discussed. 


The difference between the two long numbers actually written 
out in this passage, namely, 8-16- 4- 8- 0 and 10-19- 6 1- 8, is 
310,188 days or about a day less than 10,504 lunations. The Moon 
in the first case is 11.7 days old and in the second case is 10.4 days 
old, averaging about 4 days before the full phase. But with the 
coefhcient of error observed in the count of the Supplementary Series 
these may correspond to even lunations. 


The multiplication table is concerned with parts and multiples 
of 11,960 and is tied in with five different days, namely 12 Lamat, 
1 Akbal, 3 Eznab, 5 Ben and 7 Lamat which lie in the tzolkin 
exactly 15 days apart in the order given. Four numbers, recorded 
in two columns, lead to four of these days and Forstemann suggested 
in his Commentary on the Dresden Codex that a fifth number had 
been suppressed for lack of space, namely the one leading to 5 Ben. 
This can be placed 15 days before 7 Lamat 1 Muan. Omitting the 
unnecessary repetitions of Date A, the Epoch of the Mundane era, 
we then have: | 


F 9-16- 4-10- 8, 12 Lamat 1 Muan, Jan. 11,” 49644 ee 
15 
G 9-16 4-11- 3, 1 Akbal 16 Muan, Jan. 26, 496 A.D. 25. 


15 


BUFFALO SOCIETY OF NATURAL SCIENCES 47 


9-16- 4-11-18, 3 Eznab 11 Pax, Fetenin; 6496: A.D 10.5 


eto 4-1)? S$, 12¢Lamat’ loMuan, -ojJan. 11; °496-AaD: ~ 10. 
3- 0-15- O 
eee ai-e Oo,  ) ~Lamat: 1) Muan,)) Dec. .28, 455. A.D: *.27.8 
15 subtract 
O-19-°5+ 6-13,. 5 Ben Se Kankin~ tee 15, 350A DB: 128 


The dates reaching 10 and 25 days of the Moon are full and 
_ new moon dates in the system of the Supplementary Series, but this 
circumstance alone offers little comfort. 


LUNAR COINCIDENCES RECORDED ON MONUMENTS 


At Copan an extraordinary number of monuments declare 
Katun 11 and some of these have the face of the Moon Goddess as 
title in the introducing glyph. It appears that this date nearly 
coincided with a full moon and that the still more important round 
number which is the base of the era of the Chronicles, namely 
9- 0- 0- O0- 0, 8 Ahau 13 Ceh, was also a full moon date. These 
two dates are recorded in conjunction on Stela 3 at Copan in 
connection with interesting hieroglyphs of the moon. 


But there is another date lying just one hotun before Katun 11, 
that seems somewhat more sharply adjusted to full moon. This is 
9-10-15- 0- 0, 6 Ahau 13 Mac, January 11, 388 A.D. Moreover 
it lies exactly 8 calendar years distant from 1 Ahau 13 Mac in 
significant connection with 1 Ahau 18 Kayab. The following rela- 
tion of dates contains, I believe, the key to ancient lunar calculations 


which find echo in the Dresden Codex. 


9-10-15- 0- 0, 6 Ahau 13 Mac, Jan, bi 38h yA: 
8- 2- 0 add 
, 9-11- 3- 2- 0, In Ahauw bs Mac, fan ae9 ne SOG 
1-13- 4- 0 subtract 

9 9 9-16 0, lyAhaut8 Kayati- Apr te 7 36seA: 
The first date is an actual full moon date and the second and third 
ones are hypothetical full moon dates in the distorted Lunar calendar 
of the Supplementary Series. 


Before going farther let us examine some of the correspondences 
_ between lunations and calendar years and between lunations and 
round numbers in the day count that we may have means of intelligent 

- comparison of lunar intervals in the Maya pattern. The lowest close 
adjustments between lunations and calendar years are the following. 


1 3 X 365 days = 1095 _— days | 11 X 365 days = 4015 ~— days 
C 


37 lunations = 1092.63 “ 136 lunations = 4016.16 “ 
| 8 X 365 days = 2920 = days D4 14 X 365 days= 5110 = days 


99lunations = 2923.53 ™ 173 hinations == 5108-7955; 
| 25 X 365 days =9125 = days 
E 


309 lunations =9124.95 “ 


48 VENUS AND THE MOON 


The last is remarkably close and covers a convenient period: other 
adjustments can be reached by using multiples and combinations of 
the above. 


Next we have the outstanding correspondences between lunations 
and round numbers in the Maya day count. 


Days in Period Mean Error 
( 5tuns (onehotun) = 1800. days : 
: 61 lunations = 1801.37 “ a ee Se 
1 katun = 7200. . 
° | 244 lunations = 7205.46 ~ bo 


f 5 katuns and 10 tuns = 39600. a 

& 

Re 1341 lunations = 39600.52 “ se: 
| 10 katuns and 15 tuns = 77400. : 7 

D 


2621 lunations = 77399.67 “ rot SS 
Applying these intervals to the sequence of round number dates 
in the Long Count we get pretty close correlations with full and 
new moons at the following points during the First Empire: 
APPROXIMATE FULL Moons 


13.75 


9- 0- O- O- 0, 8 Ahau 13 Ceh, Feb.. 10,. 176. A; 

9+: F-10- 0-0, 10° Abau- 8: Zap, July 14, 284 A.D. [3.9 
9-10-15- 0- 0, 6 Ahau 13 Mac, Jan..11,.388, AS 14.2 
9-11--0-. 0- O05 A: Ahau) 8. Ceh. Dec. 15, 392 A.D. 13.5 
9-16- 5- O- O, 8 Ahau 8 Zotz, June 12, ‘496 A.D. 13.6 
10- 1-10- 0- 0, 6 Ahau 8 Pop, Mar. 24, 580. A. D. 14.4 

APPROXIMATE NEw Moons 

9- 2-10- O- O, 3 Ahau 8 Cumhu, May 25, 225 Aa. Pe be | 
9- 8- 0- O- O, 5 Abau 3 Chen; Oct, 26, 333 Ars 23 
9-13-10- 0- 0, 7 Ahau 3 Cumbhu, Mar. 28, 442 A.D. 9 
9-18-15- 0O- 0, 3. Aha. ivan Sept. 24, 545 A.D. ad 
9-19- 0- 0- O, 9 Ahau 18 Mol, Aug. 29; 550 Fi 1.4 


The full moon dates, 9-10-15- 0- 0, 6 Ahau 13 Mac, January 
11, 388 A.D. and 9-11- 0- 0- 0, 12 Ahau 8 Ceh, December 15, 
392 A.D., are abundantly recorded at Copan. The first has been 
read on two important monuments, namely Stela 12, the eastern 
marker of the astronomical base line, and Stela 2, and the second 
on no less than six major monuments, namely Stelae 12, 2, 19, 23, 
13 and 3. It is also possible that this katun ending is recorded on 
Stela 10, the western marker, and on the West Altar of Stela 9. 


Stela 3, the most elaborate of the stelae named above, has two 
initial series and a statement of 13 uinals, perhaps intended to be 
subtracted from the “contemporary” date, as follows: 


BUFFALO SOCIETY OF NATURAL SCIENCES 49 


9- 0- 0- 0- 0, 8 Ahau 13 Ceh, | Feb. 10, 176 A.D. 13.7 
‘ + * * 
9-11- O- 0- 0, 12 Ahau 8 Ceh, Deestis. 392 “AUD, 13.5 
13- 0 
910-19- 5- 0, 12 Ahau 13 Kayab, Mar. 30, 392 A.D. 19.3 


This last date brings up the interesting problem of the Metonic 
cycle. The permutation of the tzolkin, so important in the Maya 
calendar, consists of 260 days while 9 lunations amount to 265.77 
days. But the difference of 5.77 days, while considerable, is applic- 
able (with a slight correction) to an entire katun because one katun 
minus one tzolkin equals 6940 days which is the Metonic cycle 
expressing the close correspondence between 235 lunations and 19 
tropical years. Therefore when the Maya astronomer priest sub- 
tracted a tzolkin from Katun 11 he recovered the phase of the 
Moon and the place in the tropical year of Katun 10. Thus: 


Mar. 30, 373 A.D. 


9-10- 0- O- 0, 1 Ahau 8 Kayab, 18.9 
19- 5- 0 

Pepe oad O15 12 Ahau 13 Kayab, Mar 304092: A2D; 19.3 

13-' 0 

aie 0-0. - 12 Ahau <8 Ceh, 1355. 


Dee Py no 2c: 


That this is not an accidental correspondence is disclosed by the 
fact that Stela I finds the same interval from Katun 11 and recovers 
thereby the original month position of Baktun 9 as well as approxi- 
mately the same phase of the Moon. Here the statement in the 
Maya calendar is: 


9- 0- 0- 0- 0, 8 Ahau 13 Ceh, Feb. 10, 176 A.D. Full Moon 
1l- 0- 0O- O 

O7tie-Q--0- 0,12 Ahau 8 Ceh, Dec. 15, 392 A.D. Full Moon 
a ale Fam) 

Wort 957.0, 10° Ahau 13 Ceh, Dec. 16, 411 A.D. Full Moon 


This is the same as saying that 2856 lunations equals 236 calendar 
years. By multiplication we find that the former amounts to 
84,339.37 days and the latter to 84,340 days, leaving a discrepancy 
Ore.05,01 a day. 


es The interval of the Metonic cycle appears more prominently 

still in calculations on Stelae A and C and Altar U at Copan, which 
involve Venus and the resettings of the astronomical base line, as 
well as on Stela F at Quirigua which relates to about the same 
subject. Considerations of these inscriptions will be taken up shortly. 


| The Maya civil calendar appears to have been inaugurated — 
about 580 B.C. when 0 Pop coincided with the winter solstice, 
and we may be permitted to look for a lunar base at about the same 
time. As it happens the second katun after the beginning of their 
day count was a round number which nearly coincided with full 


50 VENUS AND THE MOON 


moon, namely 7- 2- 0- 0- 0, 6 Ahau 18 Pop, January 9, 573 B. C.t 
It will be noted that such a base might account for the repetition of 
lunar dates on January 9. 


A point that has been stated before deserves re-emphasis. This 
is the fact that inscriptions containing dates which reach new and 
full moons have Supplementary Series that follow the dislocated 
calendar while indicating the actual coincidence with moon glyphs 
combined with ending signs which fall outside the Supplementary 
Series. Space does not permit comparisons of texts. 


Two INTERLOCKING CALCULATIONS OF VENUS AND THE MOON 


I will now direct attention to a number of inscriptions in which 
calculations of Venus and the Moon, not to mention natural and 
ceremonial stations in the tropical year are intimately interlocked. 
The important series of dates on Altar U will make an excellent 
beginning. When I made my earlier explanation of the dates on 
this monument I was unaware of the full significance of some of 
them. It seemed strange that the dates should be stretched over so 
many years to accomplish the demonstration of the base line shifts. 
This dilation is now explained by the effort to find propitious days 
of Venus and the Moon. 


ALTAR U, Copan 


Morley’s readings are followed: since these were not made with 
present arguments in view no criticism of forcing the issue on some 
points will hold. 


A 9-14-19- 5- 0, 4 Ahau 18 Muan, Feb. 4, 471 A.D. 
Moon 26.8 days old 
13- 0 
B 9-15- 0- O- 0, 4 Ahau 13 Yax, Oct. 22,5471 AD, 
Moon 21.5 days old 
ee wee 
Cc 9-15- 8-10-12, 2 Eb 0 Pop, Apr. 9, 480 A.D. 
Moon 11.8 days old 
ee 
D S15 - 9+ De 2) Ok 10 Mol, Sept. 6, 480 A.D. 
. Full moon (14.7) 
ee ae 
E 9-15- 9-10-17, 3 Caban 0 Pop, Apr. 9, 481 A.D. 
Moon 23 days old 
2-13- 0 . 
F 9-19-12- 5-17) 8) aban 10 aviae. Dec. 15, 483 A.D. 
Moon 1.5 days old 
ee 
G 9-15-12- §--0, 94 Ahan 13 Ceh, Nov. 28, 482 A. D. 
Full moon (14 days) 
* * * 
H 9-15-12- 5- 7, 11 Manik O Mac, Dec. 5, 483 A.D. 
Moon 21.5 days old 
i- O- 0-10 ; 
I 9-16-12- 5-17, 6 Caban 10 Mol, Sept: 2, 503 Asp 
Moon 23.1 days old 


1The full moon coincidence comes the day before on January 8. 


BUFFALO SOCIETY OF NATURAL SCIENCES B51 


fe: Date A is one Metonic cycle distant from 9-14- 0- 0- 0, 
6 Ahau 13 Muan, February 4, 452 A.D., when an heliacal rising 

of Venus took place in conjunction with the Moon: see also the 
calculations on Stelae C and A for this date. 


Dates B and H. Same phase of the Moon reached in both. First 
date important in Venus calendar. 


Date D. Here we have 10 Mol (compare 6 Caban 10 Mol) 
September 6 (compare April 5, its reciprocal on the first base line 
arrangement and the inferior conjunction of Venus reached by the 
initial series date of Stela A) anda full moon. One original marker 
of the base line (Stela 10) has 9-10-19-13- 0, 3 Ahau 8 Yaxkin, 
September 6, 392 A.D. just after new moon’ (1.4) and the other 
marker (Stela 12) has 2 approximate full moon dates at 9-10-15- 0- 0, 

6 Ahau 13 Mac, January 11, 388 and 9-11- 0- 0- 0, 12 Ahau 8 Ceh, 
December 15, 392. 


Dates E and I. A Maya new year’s day with the Moon 23 days 
old is tied in with the reciprocal base line date with the moon 23.1 


days old. 


Date F. Here we have 10 Mac, comparable to the 13 Mac of 
—9-10-15- O- 0, January 11, 388 A.D. on December 15, the position 
in the natural year of 9-11- 0- 0- 0, 12 Ahau 8 Ceh, December 15, 
392 A.D. The Moon’s phase is that of the September 6 date of 
Stela 10. 


Date G. 13 Ceh, a full moon date comparable to the full moon 
date on 13 Ceh at 9- 0- 0- 0- 0, 8 Ahau 13 Ceh, February 10, 
176 A.D. Also compare 8 Ceh, the full moon date at Katun 11 

and 9-11-19- 5- 0, 10 Ahau 13 Ceh, December 16, 411 A. D., a full 
moon date recorded on Stela I. 


Date I. The date of the astronomical congress at Copan, 
recorded more frequently than any other date at this city. The 
reciprocal date of April 9 reached i in C and D. The Moon the same 
phase as Date D. 


STELA C, CopAN 


| This stela refers to interlocking counts of the Moon and of 
_ Venus, as the Moon and Venus titles in the two introducing glyphs 
plainly indicate. The dates are: 

Ase 9-14- 0-0-0, = .6: Abau 13 Muan, Feb. 4, 452 A.D. 

Moon 26.4 days old 


=< 11-14- 5- 1- 0 subtract 
Seep. 10-19-14-17- 0, 6 Ahau 18 Kayab; ~ Apr. 12, 4165 B.C. 
et Moon 24.5 days old 


*%* % % 


1This may be the observed new moon, that is the first visibility after conjunction. 


52 VENUS AND THE MOON 


a, 9-14-19- 5- 0, 4 Ahau 18 Muan, Feb. 4, 471 A.D. 
Moon 26.8 days old 

D 9-14- 6 7- 0, 5 Ahau 18 Uo, May 23, 458 A.D. 
Moon 23.3 days old 

E 9-14- 9 5- 0, 5 Ahau 8-Cumhu, “Mar. 28, 46iAteee 
New moon 

F 9-14-18-10- 0, 4 Ahau 18 Uo, May 20, 470 A.D. 
Moon 2.4 days old 


These dates will now be taken up seriatim. 


Date A. An actual heliacal rising of Venus which coincides 
with the end of a katun. It was the closest of a remarkable series 
of such coincidences, at intervals of 3 katuns, which took place at 
the height of the First Empire. The Moon on this day was a dis- 
appearing crescent (aged 26.4 days) rising before sunrise in fairly 
close conjunction with the morning star. 


Date B. The long distance number amounts in years to 4165 
-+ 452 or 4617 years less 68 days. This number of years is 19 times 
the 243 year cycle of Venus and the tropical year, and 243 times 
the Metonic cycle of the moon and tropical year. Both of these 
cycles are slightly over the times of the phenomena and in the term 
covered Venus would recede about 38 days and the moon about 75.7 
days. April 12 and 18 Kayab are both original calendarial positions 
of Venus, one in the tropical year and the other in the Maya year. 
But lunations are such short periods that correspondences within them 
carry no factor of safety especially over such a long period. As 
regards Venus other circumstances must be taken into consideration. 
Within the limits of dates on Stelae C and A there took place 
heliacal risings of Venus as morning star in positions which are 

distinctly of interest in connection with the record before us. 

9-14- ea 4- 5, 1 Chicchan- 3 Uayeb, . Apr. 1454554 
9-14-11- 
8- 

9-14-19- 8- 5, 4 Chicchan 3 Uayeb Apr. 10, 471e AS 
Perhaps by close calculation the last of these can be reduced to 
3 Kan 2 Uayeb, April 9. It will be observed at once that while 
the dates for the actual positions of Venus agree with an original 
calendarial position in the natural year (that of 19 Xul on April 12) 
the dates in the Maya year fall some 25 days after 18 Kayab. In 
the Venus table of the Dresden Codex we find 1 Ahau 18 Kayab 
on April 12, far from any current appearance of Venus, exactly 

one century from the middle date: 


9- 9 9-16 0, 1 Ahau 18 Kayab, -Apr. 1273635 2ee 
Venus table, Dresden Codex 


, 


way 


O 
5, .9 Chicchan 3 Uayeb, ~ Apr...12)546enr or 
0 


ra 


Ie bar Sa 
9-14-11- 6- 5, 9 Chiechan 3 Uayeb, Apr, 12;°403— Aue 
Heliacal rising of Venus 


BUFFALO SOCIETY OF NATURAL SCIENCES 53 


We leave for the present the consideration of this date in the distant 
-___ past and its current analogies. 


Date C. This date was read by Morley on a much effaced 
portion of Stela C. It also occurs on Stela A and appears to be 
the hidden starting point of Altar U. The interval is that of the 
_ Metonic cycle from Katun 14 and the same phase of the Moon is 
-_ recovered within 0.3 of a day. 


Date D. In connection with Date D we will consider E, F, C 
and several other numbers, the intervals between which have inter- 
esting sets of common factors. Date C is also concerned and there 
is still another date, 9-15- 1- 8- 0, 4 Ahau 8 Cumhu, March 25, 
473, probably recorded on Stela A, and almost certainly to be under- 
stood here. The Arabic numbers formed by reducing these declara- 
tions are: 3 2 Be 


D sa Aha 18) Uo, 1,399,100 
wus 5 Ahau 8 Cumhu, 1,400,140 
re 4 Ahau 18 Uo, 1,403,480 

eS 4 Ahau 18 Muan, 1,403,740 

G 4 Ahau 8 Cumhu, 1,404,520. 


Here D and E have the same day, 5 Ahau, which means that their 
_ difference is divisible by 260. Also F, C and G have differences 
divisible by 260 since they return to 4 Ahau. In addition D and 
F have a difference divisible by 365 and the same is true of E and G, 
which also reach the identical month positions in the calendar year 
of the Mayas. In the case of G we find the 74th calendar round 
repetition of the epoch of the Mundane era, 13- 0- 0- 0- 0, 4 Ahau 
8 Cumhu, October 13, 3,373. The Maya astronomers were doubtless 
developing a number of cross references between the four time counts 
of the Maya calendar year, the true or tropical year, the Venus 
calendar and the Lunar calendar. It will be seen, for instance, that 
5 Ahau 18 Uo is first shifted to 5 Ahau 8 Cumhu, the day remaining 
the same while the month changes. Then the day changes from 
5 Ahau to 4 Ahau while the month position remains fixed. 


Date D can be compared as regards lunar correspondence with 
two most important dates at Copan, namely those reached on Altar U 
which relate to the second setting of the astronomical base line. 
Beer, C 9-14. 6- 7-0, 5 Ahau 18 Uo, May 23, 458 A.D., 
5 aia ; Moon 23.3 days old 
Altar U C5290 40-17..- 3 Caban-' 0 Pop, Apr.” 9, 481. A: D., 
“tae Moon 23 days old 


A GI Bete s-t 1-2 6, Caban. (10 Mol esept, 2, 503° AsD., 
Moon 23.1 days old 


Date E. That this is no accidental similarity as regards the 
handling of intervals of entire lunations must appear when we turn 
attention to Date E on Stela C. This has the Metonic cycle 


a *).. 
Ie 
a 


54 VENUS AND THE MOON 


interval from the round number 9-13-10- 0- 0, which coincided with 
the true new moon. Thus, 


9-13-10- 0- 0, 7 Ahau 3 Cumbhu, Mar. 28, 442 A. D., 
Moon 0.3 of a day old 
19-570 
9-14- 9- 5- 0, 5 Ahau 8 Cumbhu, Mar. 28, 461 A. D., 
Moon 0.0 of a day old 


In other words true new moon coincidences are brought into the 
calculation. These should be compared with two statements of the 
full moon on Altar U, one falling on September 6, the autumnal 
station of the first setting of the astronomical base line at Copan. 
Stelae 10 and 12 record new and full moon dates and these monu- 
ments are the ones which define the base line, originally set for 
April 5 and September 6. 


Date F. This last date in the list of Stela C reaches, as does 
Date D, the Maya month position 18 Uo which appears in the 
Venus table of the Dresden Codex, possibly as a date of lunar 
significance. It is just two Metonic cycles distant from the end of 
Katun 13, thus: 

9-13- 0- 0- 0, 4 Ahau 8 Uo, May 19, 432 A.D., 
Moon 2.3 days old 
1-18-10- 0 j 
9-14-18-10- 0, 4 Ahau 18 Uo, May 20, 470 A.D., 
Moon 2.4 days old 


The summary may now be given: 


A. Heliacal rising of Venus in conjunction with Moon 26.4 days 
old counting from midnight, or zero hour of February 4, 452. 

B. A date in the distant past involving two calendarial positions 

of Venus and a correlation between the Metonic cycle and the 

Venus cycle of 243 years. . 

A. date one Metonic cycle distant from the first date. | 

A date reaching the same phase of the Moon (20.3 days after 

new moon) as do the two most important dates on Altar U. 

A date one Metonic cycle after 9-13-10- 0- 0 and like that 

reaching the new moon exactly. 

A date two Metonic cycles after 9-13- 0- 0- 0, and declaring 

a lunar position 2.4 days after the new moon. 


ee ree 


THREE ACHIEVEMENTS OF QUETZALCOATL 


I will close this analysis of significant Maya dates by discussing 
three problems in astronomy and chronology which seem to have been 
solved by the Toltec conqueror named Quetzalcoatl who is given 
credit for inventing the Mexican calendar and system of writing and 
for having compiled a sacred book containing historical and astro- 
nomical and ceremonial lore. He is also said to have inaugurated 
the ceremony of the Sacred Fire held every 52 years. The third 


BUFFALO SOCIETY OF NATURAL SCIENCES 55 


activity was in connection with a cult of the planet Venus which 
he favored and it is said that when he died on a day 1 Acatl his 
soul rose in the east as the morning star. We have reason to believe 
that these activities of Quetzalcoatl merely reflect his skill in making 


=" aN ZP 

4 : « \) ccacz > 

Fic. 9. VENUS IN CONJUNCTION WITH CONSTELLATIONS OF 
THE MAYA ZODIAC. 


On Eastern Facade ot the Nunnery at Chichen Itza. This facade deals with 
the apotheosis of Quetzalcoatl. | 


Maya science and religion available to the Mexican peoples who 
spoke a very different language from Maya. 


I. FOUNDING THE TOLTEC ERA 


The majority of the years counts in Mexican documents of high 
credibility go back to a year 1 Tecpatl, 1168 A. D. when the Toltecs 
were still ruling in the highlands of Mexico.t Other counts start 
from a year 2 Acatl, 1195 A. D., which is associated with the tying 
up of years and the new fire ceremony. Quetzalcoatl was in Yucatan 
in the second half of the Twelfth century, conquering Chichen Itza 
in 1191 A.D. A diagram of the Mexican year-bearer cycle of 52 
years with each successive year counted counter-clockwise on a wheel 
and with Tecpatl in the north, Acatl in the east, etc., is explained 
by Sahagun who says:° “The circle inscribed above is the manner of 
counting the years. It is a very ancient thing. The invention of 
it is attributed to Quetzalcoatl.” 


In the Reduction of Mayan Dates I was able to show that the 
Maya and Mexican calendars exactly correspond except for two 
shifts, which are relatively unimportant. First, that the 5 intercalary 
days were inserted several months earlier in the Mexican calendar 
than in the Maya. Secondly, that there is a fault of one day in the 
synchronization of days whose names have the same meaning. Thus 

1 Tecpatl of the Mexican calendar actually falls the day before 
1 Eznab of the Maya calendar with which properly it should 


correspond. ; 


1There is some slight use of a year count which begins with 1 Tecpatl, 1220, 
one 52 year cycle later, at the time when the Toltec empire was breaking up and most 
of the large cities were being abandoned. This is the era of Toltec Dispersal. 


2 Bernardino de Sahagun, Histoire générale des Choses de la Nouvelle-Espagne 
Trans. Jourdanet and Siméon, Paris, 1880, p. 493; and portfolio of illustrations copied 
under direction of F. de Paso y Troncoso, Florence, 1922, Codex Florentino, P. C. XLV 


56 VENUS AND THE MOON 


Thus 1 Tecpatl 1 Toxcatl of the Mexican calendar is equal in 
construction to 1 Eznab 6 Muan of the Maya calendar but it corre- 
sponds in time to the preceding day 13 Caban 5 Muan. For the 
occurrence in 1168 we have, in terms of the Maya Long Count, © 
11-10- 6-16-17, 13 Caban 5 Muan, August 6, 1168 A.D. This is 
an exact recapitulation of the epoch of the Historical era of the 
Mayas, which was 7- 0- 0- 0- 0, 10 Ahau 18 Zac, August 6, 613 
B.C. In other words, Quetzalcoatl began his own historical era 
exactly 1781 true years after the Mayas began theirs. This remark- 
able coincidence is not accidental but is in keeping with the dis- 
closures made in the inscriptions at Chichen Itza and Uxmal 
belonging to the time of Quetzalcoatl. 


Il. THE CEREMONY OF THE SACRED FIRE 


The second chronological base date that appears in the manu- 
scripts of Mexico is the one from which the ceremony of tying up 
the years and lighting the sacred fire is calculated. The year, in 
this case, is 2 Acatl, beginning in 1195 A.D. As a point of 
departure in history this chronological base is generally identified with 
the fabled Seven Caves. The year count of the Codex Vaticanus A 
begins here and so also did that of the Telleriano-Remensis following 
the same model, although the initial page is now wanting. 


The count from 2 Acatl is a carrying over of the sacred fire 
ceremony of the Mayas with a skillful readjustment. The proof 
of this is found in ceremonial days in Mexico and Yucatan connected 
with Quetzalcoatl on the one hand and with the sacred fire on the 
other, which are exactly correlated. 


Sections 2 and 3 of the Mexican tonalamatl in the Telleriano- 
Remensis Codex relate to Quetzalcoatl. The day 7 Acatl is declared 
in the gloss of the latter section to be especially lucky. Under the 
picture is this important statement: 


‘“Topiltzin Quetzalcoatl was born on the day 7 Acatl and on the days of 
7 Acatl at intervals of 52 years a great feast was held in Cholula to which 
people came from all the land and from all nations bringing great gifts to 
the lords and priests of the temple and the same occurs on the day when he 
died or went away which was 1 Acatl.” 


We need not be concerned greatly whether Quetzalcoatl could 
have invented a calendar and then signalized in it the date of his 
own birth, remembering that great characters in religion are given 
natal days on ceremonial grounds. We are reminded, for instance, 
that the birth of Christ was referred by the early Christians to 
December 25, the position of the winter solstice during the first years 
of the Julian calendar and the date of the Mithra feast of Sol invictus. 
The thing that is important in this case is that the interval of 
celebration was 52 years, or an exact calendar round. 


BUFFALO SOCIETY OF NATURAL SCIENCES 57 


Proceeding on the pecahility that this day 7 Acatl' was in the 
year 2 Acatl, and that the new fire and the tying up of the years 
took place Beniiustead of on the very day 2 Acatl with which the. 
_ year commenced, we find such a day 7 Acatl as the first day of the 

- month Panguetzaliztli. Making the same one day offset explained 
__ above we find the relation between the Toltec era of 1168 and this 
_ day 7 Acatl in terms of the Maya Long Count, to be 


= 1 Tecpatl 1 Toxcatl = 11-10- 6-16-17, 13 Caban 5 Muan, 
25 Aug. 6, 1168 A.D. 


- : Iv 7+ 6-15 
Rede vicatl 1 -Toxcatl == 11-11-14 5-12, 1 Eb 5 Muan, 
July 31, 1195 A.D. 
10- 0 


7 Acatl 1 Panquetzaliztli = 11-11-14-15-12, 6 Eb | 0 Yaxkin, 
: Feb. 16, 1196 A.D. 


. 


_ In other words we reach the Maya month position 0 Yaxkin 
pear. the original beginning of the farmer’s year. Let us now turn to 
_ Landa’s account of a ceremony in Yucatan. 


“In the tenth chapter has been related the arrival of Kukulcan,? after 
which there were some Indians who said that he had gone to heaven with 
the gods, and on this account they regarded him as a god and fixed a temple 
for him in which they should celebrate a festival to him as a god, and this 
was celebrated throughout all the land until the destruction of Mayapan. 
After this city was destroyed, it was celebrated only in the province of Mani, 
and the other provinces in gratitude for what they owed to Kukulcan, 
_ presented to him, one one year and another another, at Mani, sometimes 
— four and sometimes five magnificent banners of feathers with which they 
_ solemnized the feasts in the following manner, and not like the other ones. 


“On the 16th of the month Xul all the priests and lords of Mani 
assembled, and with them a large multitude from the towns, who came 

already prepared by fasts and abstinences. On the evening of that day they 
went forth with a great procession of people, and went with a large number 
of the comedians from the house of the lord where they were assembled. 
They proceeded very quietly to the temple of Kukulcan, which they had 
already adorned in proper fashion, and having arrived there and made their 
prayers, they placed the banners on the top of the temple. Then they all 
_ spread out their idols in the courtyard, each for himself on tree leaves which 
he had for this purpose. And having obtained new fire they began to burn 
their incense in many places and to make offerings of cooked food without 
salt or pepper, and of drinks made of beans and the seeds of gourds. The 
lords and those who had fasted remained there without returning to their 
houses for five days and five nights in prayer, always burning copal and 
engaged in their offerings, and executing several sacred dances. Until the 
first day of Yaxkin the comedians went for their findings among the principal 
houses, playing their pieces, receiving the gifts which were offered to them. 
They carried all of these to the temple and when the five days were ended 
and past, they divided the gifts among the lords, priests and dancers, and 
oa Sot. together the banners and idols again and carried them to the house of 
the prince. And then each. one went to his own home. They said, and 
4 considered it certain, that Kukulcan came down from heaven on the last 


t 


bes There are several sculptures which picture the day 7 Acatl in relation to 
Quetzalcoatl. 


2 This is etymologically equivalent in the Maya language to the name Quetzalcoat] 


58 VENUS AND THE MOON 


day of these five days and received their services, their fasts au 
They called this festival Chicckaban.” os 


the Mayas and Aztecs, to the same ie in the initial position mot 
same month. Beet 


the era of the Chronicles into the scope of denen 
fire ceremony was surely celebrated in connection with this er 
also at other times. | Bt 
(c) The Maya ceremony in which feather banners were 1 
is in agreement with the Mexican name Panquetzaliztli, month of 
the Feather Banners. At the time of the Pete. eu! es was 


Panquetzaliztli suggests that the ceremony may once have b 
in the Valley of Mexico. 


III. QUETZALCOATL AND THE VENUS CALENDAR 


Quetzalcoatl is said to have died on a day 1 Acatl 
guise as God of the Planet Venus he is pictured in conjunctio 
the sign 1 Acatl. Also there was a belief that this 1 Acatl 1 
the year 1 Acatl, hence his fabled return was confused 
coming of Cortes, for 1519 was such a year. But the ye: 
of Quetzalcoatl’s death was none other than the ae 
corresponding in part to 1208 A. D. Re ak 


What happened in the year 1 Acatl, or on the. da ct 


that can be involved in the myth of Quetzalcoatl anc 
Venus? Calendar B of the Dresden Codex _was bee: 


ancient positions of the Venus eafendaa and sien an “hella 
took place on the Maya date 11-12- 7- 3-12, 13 Eb 0 Y 
13, 1208 A. D. Remembering the one day discrepancy be 
Maya tzolkin and the Mexican tonalamatl the day 13 I 
chronologically equivalent, not with its cognate 13 Ma 
with the following day 1 Acatl. All the conditions o 


BUFFALO SOCIETY OF NATURAL SCIENCES. 59 


a 
hc ae 
on 3G LPO 


_ zalcoatl legend are justified for the Toltec overlord died—perhaps 
he was slain—on the 1 Acatl 1 Itzcalli, the first day of the fourteenth 
month in the year 1 Acatl. There is a well known statement in the 
Annals of Cuauhtitlan concerning the fatalities that .the first vision 
of Venus at heliacal rising as morning star brings about: “on the 
_ day Acatl it shoots the kings”. 


_ The order in which the Aztec cycle called Ueuetiliztli, and 
meaning the age, was counted after this beginning was identical with 
the 104 year permutation of the Maya. Whether the Mexicans 
used the supplementary shift of 12 days forward in the month at 
the end of 251 years is doubtful. The five days of beginning are 
generally arranged Cipactli, Acatl, Coatl, Olin and Atl, the formal 
permutation beginning from or with 1 Cipactli. This would be 
equivalent to using the Maya position 13 Ahau as the point of 

departure. Perhaps 1 Cipactli was chosen because of its schematic 
importance as the first day of the Mexican tonalamatl rather than 
because of its chronological equality to Ahau. But counting back 
7592 days, or 13 Venus revolutions, from the disclosed beginning 
of Quetzalcoatl’s calendar brings us to the following position in the 
Maya system: 


11-12- T- Sal el Eb On Yax, Apt. 13,212082 AD 
Pee ates ih) 2) subtract 
Piette -G6- 2-07. 13, Ahau 13 Mac, Joly lis? ASD: 


In other words if the Mexican count of Venus is made to depart 
_ from a day Cipactli it falls into accord with Calendar B of the 
Dresden Codex. 


CONCLUSIONS 
. te conclusions drawn from this study are 


use That the Maya calendars of Venus and the Moon were 
a “pnconected patterns of intervals. 

2, That the ceremonial days were those of the original settings, 
oa) in the Maya year, b in the tropical year. 

_ 3. That actual phases of Venus and the Moon were sometimes 
recorded on dates of multiple significance: a on round numbers in 
_ the day count, b on natural points of the tropical year (equinoxes, 
~ solstices, astronomical base line dates, true anniversaries of the epochs 
of oe eras, etc.). 

+ ee That the principal purposes must have been religious or 


ee F. That the correlation explained in the Reduction %, Mayan 
Date is accurate and sufficient to solve the astronomical data of the 


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TABLE Or CONTENTS PAGE 

a REE He a ae ele 3 

| se Rl IRA 5 

ke Maya Calendars Shoat Intercalation...:.......... bb si BOL nates. Sm 6 
er Meret tatural Basis of the Vemus  Calemdaricccccsscscccssssmusecmsecsssnsencesnee 9 
How the Mayas Formalized the Venus Ephemeris..cecscccsssssssussseeen 11 
Placing the Venus Table in PXCOAAL EN EONOLO CY ed cleantech 14 
References to Venus in Ancient PGeT OCs ee eres a, 16 
Round Numbers that Coincide with Appearances of Venus........ 18 
The Inauguration of the Venus Calendar. nmemennnmnmnemnenmnmnenanne 19 
TV aes aise chile ncn nny spmscndbcnclane seeped ee peenetel 22 
Other References to Venus in Ancient Inscriptions... 24 

3 A ica gaa ese sieasieccinedtuonantricler 24 
Be ANC Ula t1ONS = ts SY AX CHA oie a saccnloslcoacesovomnnnsininanctasonmbnononcon 24 

2 ieee nse Lemples Of Copan ce ccd esscnemcseseisecadénssttnlasericyccee 2 
tesa togster Altars at Copatn mecca ieceneewnernnmqnenieesneeirpin 27 
Other Uses of the Venus Monster Moti vernnnnennnnnnnnnn shies 29 
Mime amber Approximations. ci cccccnwwcwesrseneieninsiecientermcins eit 
Title ee a ee Nee ee ta 33 
4 ; Further Examples of Inscriptions Dealing with Venus..csssesess 36 
The Lunar Oe ee ee a ee eet at eee che AD 
The Supplementary SE ets hs Daf rch AN te OMIM CfA ic Saale OR 42 
Interrelations in Tables of Venus and the Moom.ressncnuseemenee 44 
Lunar Coincidences Recorded on Monument s.crucnnunnstnnsnnsne 47 
Two Interlocking Calculations of Venus and the Moonen 50 

| Bxdeare UU, COPA De cinscneen ie em Ne 2 SAE SOM A, Sent ein eaece ee Tt art 50 

a eS SUSE TA ab I led en enc Aen tm Se hb ata Soe) LR eR 51 
Three Pap mewenetitsn Gt (NetZalCOat hia: oie nr te hey 54 
x Per ourmine thet oltece hia tak a ere con 35 
Ram ne Ceremony of the Sacred: Tire. eet 56 

Ti -Gyoetzalcoatl and the, Venus Calendar. 58 

e Conclusions SU a MRO EO AER SS CH en ee SONA 2 ec alot eal tee 59 


LIST OF ILLUSTRATIONS 

‘hay PAGE 
. Passage on the Hieroglyphic Stairway at Naranjo......... 16 
Dee 5 Meee Onc otela A 2 at Ua xa ct uttiintencrcincnsciustanscsansioncs 18 
(SRA SHINE Ara lig en eR 22 
Meiea-face on Lintel 4 at Piedras Negrasicc ns cceeeccsscoutsscsiscaicmn 23 
Title Glyphs of the Summer Solstice..cccccscccsnese ce 33 
Title Glyphs of the Ceremonial Fire... esses ee Ae a5 

Bere criptionion AltarsS at, Copan. sk cadeabdacoceomin ah 


“Og Fire and Imix-Ahau Glyphs at Katuns 14 and 17. 38 
_ Venus i in Conjunction with Constellations of the Maya 


Zodiac Cie Pega tok ere AS GE ates ee AE ae N Sa 


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